Showing 1–50 of 65 results for author: Schmitt, A

Phases and properties of color superconductors

Authors: Andreas Schmitt

Abstract: Cold and dense matter is expected to be in a color-superconducting state. Here we review two calculations, relevant for fundamental properties and applications of color superconductivity, respectively: the weak-coupling QCD calculation of the fermionic energy gap together with the magnetic screening masses of the gauge bosons, and the calculation of bulk viscosity from a non-leptonic electroweak p… ▽ More Cold and dense matter is expected to be in a color-superconducting state. Here we review two calculations, relevant for fundamental properties and applications of color superconductivity, respectively: the weak-coupling QCD calculation of the fermionic energy gap together with the magnetic screening masses of the gauge bosons, and the calculation of bulk viscosity from a non-leptonic electroweak process. These calculations are supplemented by a discussion of color superconductors with mismatched Fermi momenta, and they are embedded in the context of the state of the art by giving an overview of previous and ongoing work and future directions. △ Less

Submitted 10 November, 2025; originally announced November 2025.

Comments: 40 pages, 9 figures, prepared for "Encyclopedia of Nuclear Physics"

Nuclear chiral density wave in neutron stars?

Authors: Orestis Papadopoulos, Andreas Schmitt

Abstract: Anisotropic phases potentially play a role in the internal composition of neutron stars, the main laboratory for the phase structure of QCD at high baryon densities. We review the study of such a phase, the chiral density wave, within a phenomenological nucleon-meson model, including nucleonic vacuum fluctuations within a renormalization scheme recently developed. Neutron stars in this model and w… ▽ More Anisotropic phases potentially play a role in the internal composition of neutron stars, the main laboratory for the phase structure of QCD at high baryon densities. We review the study of such a phase, the chiral density wave, within a phenomenological nucleon-meson model, including nucleonic vacuum fluctuations within a renormalization scheme recently developed. Neutron stars in this model and within our approximations either do not contain a chiral density wave core or they are too light to agree with observations. △ Less

Submitted 6 November, 2025; v1 submitted 12 September, 2025; originally announced September 2025.

Comments: 12 pages, 4 figures, contribution to proceedings of XQCD 2025, July 2-4; v2: small modifications to the text, matches published version

Softening holographic nuclear matter

Authors: Christian Ecker, Nicolas Kovensky, Orestis Papadopoulos, Andreas Schmitt

Abstract: Baryons in the holographic Witten-Sakai-Sugimoto model are described by instanton solutions on the flavor branes. A commonly used approximation for dense baryonic matter replaces the many-instanton solution by a simpler, spatially homogeneous, ansatz, which requires a discontinuity in the holographic direction of the non-abelian gauge field in order to account for topological baryon number. We poi… ▽ More Baryons in the holographic Witten-Sakai-Sugimoto model are described by instanton solutions on the flavor branes. A commonly used approximation for dense baryonic matter replaces the many-instanton solution by a simpler, spatially homogeneous, ansatz, which requires a discontinuity in the holographic direction of the non-abelian gauge field in order to account for topological baryon number. We point out that the simplest configuration with a single jump - often used in previous studies - results in matter at saturation density that is much stiffer than real-world nuclear matter. This is improved, although not completely remedied, by adding a second jump. We present a systematic discussion of all possible configurations up to four jumps, dynamically computing locations of and behavior at the discontinuities. We find solutions that continuously connect to those based on pointlike baryons, thus, for the first time, establishing a concrete link between the instantonic and homogeneous pictures. This is supported by translating the multi-jump profiles of the gauge field into gauge invariant multi-layer charge distributions. The most important of our novel configurations has a block-like structure in the bulk, becomes pointlike at low density and/or large coupling, and is energetically preferred over all previously studied configurations. Therefore, our work lays the ground for improved predictions from holography for dense nuclear matter in neutron stars. △ Less

Submitted 2 September, 2025; originally announced September 2025.

Comments: 41 pages, 11 figures

How neutron star properties disfavor a nuclear chiral density wave

Authors: Orestis Papadopoulos, Andreas Schmitt

Abstract: Cold and dense matter may break rotational symmetry spontaneously and thus form an anisotropic phase in the interior of neutron stars. We consider the concrete example of an anisotropic chiral condensate in the form of a chiral density wave. Employing a nucleon-meson model and taking into account fermionic vacuum fluctuations, we improve and extend previous results by imposing the conditions of el… ▽ More Cold and dense matter may break rotational symmetry spontaneously and thus form an anisotropic phase in the interior of neutron stars. We consider the concrete example of an anisotropic chiral condensate in the form of a chiral density wave. Employing a nucleon-meson model and taking into account fermionic vacuum fluctuations, we improve and extend previous results by imposing the conditions of electric charge neutrality and electroweak equilibrium, by allowing for a more general form of the vector meson self-interactions, and by including properties of pure neutron matter into the fit of the model parameters. We find that the conditions inside neutron stars postpone the onset of the chiral density wave to larger densities compared to isospin-symmetric nuclear matter. While this still allows for the construction of stars with an anisotropic core, we find that the chiral density wave is energetically preferred only in a corner of the parameter space where matter is too soft to generate stars with realistic masses. Therefore, taking into account constraints from astrophysical data, our calculation predicts an isotropic neutron star core. △ Less

Submitted 21 January, 2025; v1 submitted 12 November, 2024; originally announced November 2024.

Comments: 21 pages, 7 figures; v2: two new panels added in Fig. 2, minor improvements to the text, references added, to appear in PRD

Thermal pion condensation: holography meets lattice QCD

Authors: Nicolas Kovensky, Andreas Schmitt

Abstract: The holographic Witten-Sakai-Sugimoto model is often employed to describe strongly-coupled baryonic and isospin-asymmetric matter, for example in the context of neutron stars. Here we consider the case of vanishing baryon chemical potential, where detailed comparisons to data from lattice QCD are possible. To this end, we extend previous works by including a realistic pion mass and pion condensati… ▽ More The holographic Witten-Sakai-Sugimoto model is often employed to describe strongly-coupled baryonic and isospin-asymmetric matter, for example in the context of neutron stars. Here we consider the case of vanishing baryon chemical potential, where detailed comparisons to data from lattice QCD are possible. To this end, we extend previous works by including a realistic pion mass and pion condensation into the decompactified limit of the model and evaluate the system for arbitrary isospin chemical potentials and temperatures. After suitably fixing the 3 parameters of the model, we find that the overall phase structure is in excellent agreement with lattice results. This also holds for observables at low temperatures in the strongly coupled regime, while we discover and discuss some discrepancies at large temperatures. Our findings give reassurance for the validity of previous and future applications of this model and highlight the aspects where improvements are needed. △ Less

Submitted 22 October, 2024; v1 submitted 17 July, 2024; originally announced July 2024.

Comments: 33 pages, 9 figures; v2: new panel added in figure 9, showing the pion mass dependence of the phase diagram; references added; version accepted for publication in JHEP

Chiral Soliton Lattice turns into 3D crystal

Authors: Geraint W. Evans, Andreas Schmitt

Abstract: Chiral perturbation theory predicts the chiral anomaly to induce a so-called Chiral Soliton Lattice at sufficiently large magnetic fields and baryon chemical potentials. This state breaks translational invariance in the direction of the magnetic field and was shown to be unstable with respect to charged pion condensation. Improving on previous work by considering a realistic pion mass, we employ m… ▽ More Chiral perturbation theory predicts the chiral anomaly to induce a so-called Chiral Soliton Lattice at sufficiently large magnetic fields and baryon chemical potentials. This state breaks translational invariance in the direction of the magnetic field and was shown to be unstable with respect to charged pion condensation. Improving on previous work by considering a realistic pion mass, we employ methods from type-II superconductivity and construct a three-dimensional pion (and baryon) crystal perturbatively, close to the instability curve of the Chiral Soliton Lattice. We find an analogue of the usual type-I/type-II transition in superconductivity: Along the instability curve for magnetic fields $eB > 0.12\, {\rm GeV}^2$ and chemical potentials $μ< 910\, {\rm MeV}$, this crystal can continuously supersede the Chiral Soliton Lattice. For smaller magnetic fields the instability curve must be preceded by a discontinuous transition. △ Less

Submitted 26 January, 2024; v1 submitted 7 November, 2023; originally announced November 2023.

Comments: 32 pages, 7 figures; v2: small addition to the outlook, references added, version to appear in JHEP

Chiral crossover vs chiral density wave in dense nuclear matter

Authors: Savvas Pitsinigkos, Andreas Schmitt

Abstract: We employ a model based on nucleonic and mesonic degrees of freedom to discuss the competition between isotropic and anisotropic phases in cold and dense matter. Assuming isotropy, the model exhibits a chiral phase transition which is of second order in the chiral limit and becomes a crossover in the case of a realistic pion mass. This observation crucially depends on the presence of the nucleonic… ▽ More We employ a model based on nucleonic and mesonic degrees of freedom to discuss the competition between isotropic and anisotropic phases in cold and dense matter. Assuming isotropy, the model exhibits a chiral phase transition which is of second order in the chiral limit and becomes a crossover in the case of a realistic pion mass. This observation crucially depends on the presence of the nucleonic vacuum contribution. Allowing for an anisotropic phase in the form of a chiral density wave can disrupt the smooth crossover. We identify the regions in the parameter space of the model where a chiral density wave is energetically preferred. A high-density re-appearance of the chiral density wave with unphysical behavior, as seen in previous studies, is avoided by a suitable renormalization scheme. A nonzero pion mass tends to disfavor the anisotropic phase compared to the chiral limit and we find that, within our model, the chiral density wave is only realized for baryon densities of at least about 6 times nuclear saturation density. △ Less

Submitted 22 April, 2024; v1 submitted 4 September, 2023; originally announced September 2023.

Comments: 22 pages, 6 figures; v2: minor clarifications, references added, version to appear in PRD; v3: typos in eqs. (17) and (34a) corrected (with no consequences for the rest of the paper)

Phases of cold holographic QCD: baryons, pions and rho mesons

Authors: Nicolas Kovensky, Aaron Poole, Andreas Schmitt

Abstract: We improve the holographic description of isospin-asymmetric baryonic matter within the Witten-Sakai-Sugimoto model by accounting for a realistic pion mass, computing the pion condensate dynamically, and including rho meson condensation by allowing the gauge field in the bulk to be anisotropic. This description takes into account the coexistence of baryonic matter with pion and rho meson condensat… ▽ More We improve the holographic description of isospin-asymmetric baryonic matter within the Witten-Sakai-Sugimoto model by accounting for a realistic pion mass, computing the pion condensate dynamically, and including rho meson condensation by allowing the gauge field in the bulk to be anisotropic. This description takes into account the coexistence of baryonic matter with pion and rho meson condensates. Our main result is the zero-temperature phase diagram in the plane of baryon and isospin chemical potentials. We find that the effective pion mass in the baryonic medium increases with baryon density and that, as a consequence, there is no pion condensation in neutron-star matter. Our improved description also predicts that baryons are disfavored at low baryon chemical potentials even for arbitrarily large isospin chemical potential. Instead, rho meson condensation sets in on top of the pion condensate at an isospin chemical potential of about $9.4\, m_π$. We further observe a highly non-monotonic phase boundary regarding the disappearance of pion condensation. △ Less

Submitted 4 October, 2023; v1 submitted 21 February, 2023; originally announced February 2023.

Comments: 31 pages, 7 figures, v3: typos corrected, version to appear in SciPost Phys; v2: new ansatz for the bulk gauge field, eliminating an unjustified assumption in v1; as a consequence, numerous modifications in text, equations, and plots, with main conclusions unchanged

Chiral restoration of strange baryons

Authors: Eduardo S. Fraga, Rodrigo da Mata, Savvas Pitsinigkos, Andreas Schmitt

Abstract: We review the results of a phenomenological model for cold and dense nuclear matter exhibiting a chiral phase transition. The idea is to model the quark-hadron phase transition under neutron star conditions within a single model, but without adding quark degrees of freedom by hand. To this end, strangeness is included in the form of hyperonic degrees of freedom, whose light counterparts provide th… ▽ More We review the results of a phenomenological model for cold and dense nuclear matter exhibiting a chiral phase transition. The idea is to model the quark-hadron phase transition under neutron star conditions within a single model, but without adding quark degrees of freedom by hand. To this end, strangeness is included in the form of hyperonic degrees of freedom, whose light counterparts provide the strangeness in the chirally restored phase. In the future, the model can be used for instance to compute the surface tension at the (first-order) chiral phase transition and to study the possible existence of inhomogeneous phases. △ Less

Submitted 22 September, 2022; originally announced September 2022.

Comments: 6 pages, 4 figures, contribution to proceedings of QCD@Work, 27-30 June 2022

Strange quark matter from a baryonic approach

Authors: Eduardo S. Fraga, Rodrigo da Mata, Savvas Pitsinigkos, Andreas Schmitt

Abstract: We construct a model for dense matter based on low-density nuclear matter properties that exhibits a chiral phase transition and that includes strangeness through hyperonic degrees of freedom. Empirical constraints from nuclear matter alone allow for various scenarios, from a strong first-order chiral transition at relatively low densities through a weaker transition at higher densities, even up t… ▽ More We construct a model for dense matter based on low-density nuclear matter properties that exhibits a chiral phase transition and that includes strangeness through hyperonic degrees of freedom. Empirical constraints from nuclear matter alone allow for various scenarios, from a strong first-order chiral transition at relatively low densities through a weaker transition at higher densities, even up to a smooth crossover not far beyond the edge of the allowed range. The model parameters can be chosen such that at asymptotically large densities the chirally restored phase contains strangeness and the speed of sound approaches the conformal limit, resulting in a high-density phase that resembles deconfined quark matter. Additionally, if the model is required to reproduce sufficiently massive compact stars, the allowed parameter range is significantly narrowed down, resulting for instance in a very narrow range for the poorly known slope parameter of the symmetry energy, $L\simeq (88-92)\, {\rm MeV}$. We also find that for the allowed parameter range strangeness does not appear in the form of hyperons in the chirally broken phase and the chiral transition is of first order. Due to its unified approach and relative simplicity - here we restrict ourselves to zero temperature and the mean-field approximation - the model can be used in the future to study dense matter under compact star conditions in the vicinity of the chiral phase transition, for instance to compute the surface tension or to investigate spatially inhomogeneous phases. △ Less

Submitted 27 September, 2022; v1 submitted 18 June, 2022; originally announced June 2022.

Comments: 24 pages, 7 figures; v2: minor improvements in the text, version accepted for publication in PRD

Chiral anomaly induces superconducting baryon crystal

Authors: Geraint W. Evans, Andreas Schmitt

Abstract: It was previously shown within chiral perturbation theory that the ground state of QCD in a sufficiently large magnetic field and at nonvanishing, but not too large, baryon chemical potential is a so-called chiral soliton lattice. The crucial ingredient of this observation was the chiral anomaly in the form of a Wess-Zumino-Witten term, which couples the baryon chemical potential to the magnetic f… ▽ More It was previously shown within chiral perturbation theory that the ground state of QCD in a sufficiently large magnetic field and at nonvanishing, but not too large, baryon chemical potential is a so-called chiral soliton lattice. The crucial ingredient of this observation was the chiral anomaly in the form of a Wess-Zumino-Witten term, which couples the baryon chemical potential to the magnetic field and the gradient of the neutral pion field. It was also shown that the chiral soliton lattice becomes unstable towards charged pion condensation at larger magnetic fields. We point out that this instability bears a striking resemblance to the second critical magnetic field of a type-II superconductor, however with the superconducting phase appearing upon increasing the magnetic field. The resulting phase has a periodically varying charged pion condensate that coexists with a neutral pion supercurrent. We construct this phase analytically in the chiral limit and show that it is energetically preferred. Just like an ordinary type-II superconductor, it exhibits a hexagonal array of magnetic flux tubes, and, due to the chiral anomaly, a spatially oscillating baryon number of the same crystalline structure. △ Less

Submitted 12 September, 2022; v1 submitted 2 June, 2022; originally announced June 2022.

Comments: 30 pages, 2 figures; v2: references added, minor improvements in the text, typo in Eq. (3.20) corrected, version accepted for publication in JHEP

Predictions for neutron stars from holographic nuclear matter

Authors: Nicolas Kovensky, Aaron Poole, Andreas Schmitt

Abstract: We discuss masses, radii, and tidal deformabilities of neutron stars constructed from the holographic Witten-Sakai-Sugimoto model. Using the same model for crust and core of the star, we combine our theoretical results with the latest astrophysical data, thus deriving more stringent constraints than given by the data alone. For instance, our calculation predicts -- independent of the model paramet… ▽ More We discuss masses, radii, and tidal deformabilities of neutron stars constructed from the holographic Witten-Sakai-Sugimoto model. Using the same model for crust and core of the star, we combine our theoretical results with the latest astrophysical data, thus deriving more stringent constraints than given by the data alone. For instance, our calculation predicts -- independent of the model parameters -- an upper limit for the maximal mass of the star of about 2.46 solar masses and a lower limit of the (dimensionless) tidal deformability of a 1.4-solar-mass star of about 277. △ Less

Submitted 20 December, 2021; originally announced December 2021.

Comments: 11 pages, 6 figures, Contribution to proceedings of XXXIII International (ONLINE) Workshop on High Energy Physics "Hard Problems of Hadron Physics: Non-Perturbative QCD & Related Quests"

Building a realistic neutron star from holography

Authors: Nicolas Kovensky, Aaron Poole, Andreas Schmitt

Abstract: We employ the recently improved description of dense baryonic matter within the Witten-Sakai-Sugimoto model to construct neutron stars. In contrast to previous holographic approaches, the presence of an isospin asymmetry allows us to implement beta equilibrium and electric charge neutrality. As a consequence, we are able to model the crust of the star within the same formalism and compute the loca… ▽ More We employ the recently improved description of dense baryonic matter within the Witten-Sakai-Sugimoto model to construct neutron stars. In contrast to previous holographic approaches, the presence of an isospin asymmetry allows us to implement beta equilibrium and electric charge neutrality. As a consequence, we are able to model the crust of the star within the same formalism and compute the location of the crust-core transition dynamically. After showing that a simple pointlike approximation for the baryons fails to satisfy astrophysical constraints, we demonstrate that our improved description does account for neutron stars that meet the current experimental constraints for mass, radius, and tidal deformability. However, we also point out tensions in the parameter fit and large-$N_c$ artifacts and discuss how to potentially resolve them in the future. △ Less

Submitted 28 February, 2022; v1 submitted 5 November, 2021; originally announced November 2021.

Comments: 19 pages, 12 figures; v2: small correction in Table I, reference added, accepted for publication in PRD; v3: typos in last line of p7 and equation (34b) corrected

Isospin asymmetry in holographic baryonic matter

Authors: Nicolas Kovensky, Andreas Schmitt

Abstract: We study baryonic matter with isospin asymmetry, including fully dynamically its interplay with pion condensation. To this end, we employ the holographic Witten-Sakai-Sugimoto model and the so-called homogeneous ansatz for the gauge fields in the bulk to describe baryonic matter. Within the confined geometry and restricting ourselves to the chiral limit, we map out the phase structure in the prese… ▽ More We study baryonic matter with isospin asymmetry, including fully dynamically its interplay with pion condensation. To this end, we employ the holographic Witten-Sakai-Sugimoto model and the so-called homogeneous ansatz for the gauge fields in the bulk to describe baryonic matter. Within the confined geometry and restricting ourselves to the chiral limit, we map out the phase structure in the presence of baryon and isospin chemical potentials, showing that for sufficiently large chemical potentials condensed pions and isospin-asymmetric baryonic matter coexist. We also present first results of the same approach in the deconfined geometry and demonstrate that this case, albeit technically more involved, is better suited for comparisons with and predictions for real-world QCD. Our study lays the ground for future improved holographic studies aiming towards a realistic description of charge neutral, beta-equilibrated matter in compact stars, and also for more refined comparisons with lattice studies at nonzero isospin chemical potential. △ Less

Submitted 28 February, 2022; v1 submitted 7 May, 2021; originally announced May 2021.

Comments: 53 pages, 8 figures, v2: minor improvements in the text, format adapted to SciPost Physics; v3: typos in Eqs.(20) and (30c) corrected

Journal ref: SciPost Phys. 11, 029 (2021)

Strange quark mass turns magnetic domain walls into multi-winding flux tubes

Authors: Geraint W. Evans, Andreas Schmitt

Abstract: Dense quark matter is expected to behave as a type-II superconductor at strong coupling. It was previously shown that if the strange quark mass $m_s$ is neglected, magnetic domain walls in the so-called 2SC phase are the energetically preferred magnetic defects in a certain parameter region. Computing the flux tube profiles and associated free energies within a Ginzburg-Landau approach, we find a… ▽ More Dense quark matter is expected to behave as a type-II superconductor at strong coupling. It was previously shown that if the strange quark mass $m_s$ is neglected, magnetic domain walls in the so-called 2SC phase are the energetically preferred magnetic defects in a certain parameter region. Computing the flux tube profiles and associated free energies within a Ginzburg-Landau approach, we find a cascade of multi-winding flux tubes as "remnants" of the domain wall when $m_s$ is increased. These flux tubes exhibit an unconventional ring-like structure of the magnetic field. We show that flux tubes with winding numbers larger than one survive for values of $m_s$ up to about 20% of the quark chemical potential. This makes them unlikely to play a significant role in compact stars, but they may appear in the QCD phase diagram in the presence of an external magnetic field. △ Less

Submitted 4 December, 2020; v1 submitted 2 September, 2020; originally announced September 2020.

Comments: 25 pages, 6 figures; v2: minor improvements, extended discussion on length scales of the flux tubes, to appear in J.Phys.G

Holographic quarkyonic matter

Authors: Nicolas Kovensky, Andreas Schmitt

Abstract: We point out a new configuration in the Witten-Sakai-Sugimoto model, allowing baryons in the pointlike approximation to coexist with fundamental quarks. The resulting phase is a holographic realization of quarkyonic matter, which is predicted to occur in QCD at a large number of colors, and possibly plays a role in real-world QCD as well. We find that holographic quarkyonic matter is chirally symm… ▽ More We point out a new configuration in the Witten-Sakai-Sugimoto model, allowing baryons in the pointlike approximation to coexist with fundamental quarks. The resulting phase is a holographic realization of quarkyonic matter, which is predicted to occur in QCD at a large number of colors, and possibly plays a role in real-world QCD as well. We find that holographic quarkyonic matter is chirally symmetric and that, for large baryon chemical potentials, it is energetically preferred over pure nuclear matter and over pure quark matter. The zero-temperature transition from nuclear matter to the quarkyonic phase is of first order in the chiral limit and for a realistic pion mass. For pion masses far beyond the physical point we observe a quark-hadron continuity due to the presence of quarkyonic matter. △ Less

Submitted 23 September, 2020; v1 submitted 24 June, 2020; originally announced June 2020.

Comments: 38 pages, 8 figures; v2: improvements in the text, references added, version published in JHEP

Chiral pasta

Authors: Andreas Schmitt

Abstract: Interiors of neutron stars are ultra-dense and may contain a core of deconfined quark matter. Such a core connects to the outer layers smoothly or through a sharp microscopic interface or through an intermediate macroscopic layer of inhomogeneous mixed phases, which is globally neutral but locally contains electrically charged domains. Here I employ a nucleon-meson model under neutron star conditi… ▽ More Interiors of neutron stars are ultra-dense and may contain a core of deconfined quark matter. Such a core connects to the outer layers smoothly or through a sharp microscopic interface or through an intermediate macroscopic layer of inhomogeneous mixed phases, which is globally neutral but locally contains electrically charged domains. Here I employ a nucleon-meson model under neutron star conditions that shows a first-order chiral phase transition at large densities. In the vicinity of this chiral transition I calculate the free energies of various mixed phases - different 'pasta structures' - in the Wigner-Seitz approximation. Crucially, chirally broken nuclear matter and the approximately chirally symmetric phase (loosely interpreted as quark matter) are treated on the same footing. This allows me to compute the interface profiles of bubbles, rods, and slabs fully consistently, taking into account electromagnetic screening effects and without needing the surface tension as an input. I find that the full numerical results tend to disfavor mixed phases compared to a simple step-like approximation used frequently in the literature and that the predominantly favored pasta structure consists of slabs with a surface tension $Σ\simeq 6\, {\rm MeV}/{\rm fm}^2$. △ Less

Submitted 30 March, 2020; v1 submitted 4 February, 2020; originally announced February 2020.

Comments: 19 pages, 8 figures; v2: minor improvements in the text, one reference added, accepted for publication in Phys. Rev. D

Journal ref: Phys. Rev. D 101, 074007 (2020)

Heavy Holographic QCD

Authors: Nicolas Kovensky, Andreas Schmitt

Abstract: We study the phase structure of the Witten-Sakai-Sugimoto model in the plane of temperature and baryon chemical potential, including the effect of a nonzero current quark mass. Our study is performed in the decompactified limit of the model, which, at least regarding the chiral phase transition, appears to be closer to real-world QCD than the original version. Following earlier studies, we account… ▽ More We study the phase structure of the Witten-Sakai-Sugimoto model in the plane of temperature and baryon chemical potential, including the effect of a nonzero current quark mass. Our study is performed in the decompactified limit of the model, which, at least regarding the chiral phase transition, appears to be closer to real-world QCD than the original version. Following earlier studies, we account for the quark mass in an effective way based on an open Wilson line operator whose expectation value is identified with the chiral condensate. We find that the quark mass stabilizes a configuration with string sources and point out that this phase plays an important role in the phase diagram. Furthermore, we show that the quark mass breaks up the first-order chiral phase transition curve and introduces critical points to the phase diagram. Similarities of the phase structure to other holographic approaches and to lattice simulations of "heavy QCD" are found and discussed. By making holographic QCD more realistic, our results open the door to a better understanding of real-world strongly coupled hot and dense matter. △ Less

Submitted 11 June, 2020; v1 submitted 19 November, 2019; originally announced November 2019.

Comments: 34 pages, 7 figures, v3: typos corrected in Eqs. (2.24), (3.2), (3.3), (3.28), and the caption of Fig 3 corrected

Dissipation triggers dynamical two-stream instability

Authors: Nils Andersson, Andreas Schmitt

Abstract: Two coupled, interpenetrating fluids suffer instabilities beyond certain critical counterflows. For ideal fluids, an energetic instability occurs at the point where a sound mode inverts its direction due to the counterflow, while dynamical instabilities only occur at larger relative velocities. Here we discuss two relativistic fluids, one of which is dissipative. Using linearized hydrodynamics, we… ▽ More Two coupled, interpenetrating fluids suffer instabilities beyond certain critical counterflows. For ideal fluids, an energetic instability occurs at the point where a sound mode inverts its direction due to the counterflow, while dynamical instabilities only occur at larger relative velocities. Here we discuss two relativistic fluids, one of which is dissipative. Using linearized hydrodynamics, we show that in this case the energetic instability turns dynamical, i.e., there is an exponentially growing mode, and this exponential growth only occurs in the presence of dissipation. This result is general and does not rely on an underlying microscopic theory. It can be applied to various two-fluid systems for instance in the interior of neutron stars. We also point out that under certain circumstances the two-fluid system exhibits a mode analogous to the r-mode in neutron stars that can become unstable for arbitrarily small values of the counterflow. △ Less

Submitted 1 November, 2019; v1 submitted 7 August, 2019; originally announced August 2019.

Comments: 20 pages, 4 figures, v2: minor changes in the text, references added, version accepted for publication

Multi-winding flux tubes in CFL quark matter

Authors: Alexander Haber, Andreas Schmitt

Abstract: Color-flavor locked quark matter can be described as a three-component superconductor and thus shows unconventional behavior in the transition regime from type-I to type-II superconductivity. We discuss this behavior by studying magnetic line defects in a Ginzburg-Landau approach, taking into account all possible values of the three winding numbers. After a brief discussion of the defects that inc… ▽ More Color-flavor locked quark matter can be described as a three-component superconductor and thus shows unconventional behavior in the transition regime from type-I to type-II superconductivity. We discuss this behavior by studying magnetic line defects in a Ginzburg-Landau approach, taking into account all possible values of the three winding numbers. After a brief discussion of the defects that include baryon circulation we focus on pure magnetic flux tubes. We show that at strong coupling, relevant for neutron stars, type-II behavior is conceivable and the most preferred configuration has minimal total winding. Only at weak coupling we find a regime where multi-winding flux tubes are preferred, although this regime most likely requires an unrealistically large superconducting gap. △ Less

Submitted 29 November, 2018; originally announced November 2018.

Comments: 12 pages, 3 figures, proceedings contribution to "XIIIth Quark Confinement and the Hadron Spectrum", 31 July - 6 August 2018, Maynooth University, Ireland

Towards a holographic quark-hadron continuity

Authors: Kazem Bitaghsir Fadafan, Farideh Kazemian, Andreas Schmitt

Abstract: We study dense nuclear and quark matter within a single microscopic approach, namely the holographic Sakai-Sugimoto model. Nuclear matter is described via instantons in the bulk, and we show that instanton interactions are crucial for a continuous connection of chirally broken and chirally symmetric phases. The continuous path from nuclear to quark matter includes metastable and unstable stationar… ▽ More We study dense nuclear and quark matter within a single microscopic approach, namely the holographic Sakai-Sugimoto model. Nuclear matter is described via instantons in the bulk, and we show that instanton interactions are crucial for a continuous connection of chirally broken and chirally symmetric phases. The continuous path from nuclear to quark matter includes metastable and unstable stationary points of the potential, while the actual chiral phase transition remains of first order, as in earlier approximations. We show that the model parameters can be chosen to reproduce low-density properties of nuclear matter and observe a non-monotonic behavior of the speed of sound as a function of the baryon chemical potential, as suggested by constraints from QCD and astrophysics. △ Less

Submitted 27 March, 2019; v1 submitted 21 November, 2018; originally announced November 2018.

Comments: 28+19 pages, 5 figures; v2: clarifications and references added, version to appear in JHEP

Surface tension of dense matter at the chiral phase transition

Authors: Eduardo S. Fraga, Maurício Hippert, Andreas Schmitt

Abstract: If a first-order phase transition separates nuclear and quark matter at large baryon density, an interface between these two phases has a nonzero surface tension. We calculate this surface tension within a nucleon-meson model for domain walls and bubbles. Various methods and approximations are discussed and compared, including a numerical evaluation of the spatial profile of the interface. We also… ▽ More If a first-order phase transition separates nuclear and quark matter at large baryon density, an interface between these two phases has a nonzero surface tension. We calculate this surface tension within a nucleon-meson model for domain walls and bubbles. Various methods and approximations are discussed and compared, including a numerical evaluation of the spatial profile of the interface. We also compute the surface tension at the other first-order phase transitions of the model: the nuclear liquid-gas transition and, in the parameter regime where it exists, the direct transition from the vacuum to the (approximately) chirally symmetric phase. Identifying the chirally symmetric phase with quark matter - our model does not contain explicit quark degrees of freedom - we find maximal surface tensions of the vacuum-quark transition $Σ_{\rm VQ}\sim 15 \, {\rm MeV}/{\rm fm}^2$, relevant for the surface of quark stars, and of the nuclear-quark transition $Σ_{\rm NQ}\sim 10 \, {\rm MeV}/{\rm fm}^2$, relevant for hybrid stars and for quark matter nucleation in supernovae and neutron star mergers. △ Less

Submitted 23 January, 2019; v1 submitted 31 October, 2018; originally announced October 2018.

Comments: 16 pages, 6 figures; v2: figure 6 improved, references added, small modifications to the text, version to appear in Phys. Rev. D

Journal ref: Phys. Rev. D 99, 014046 (2019)

New color-magnetic defects in dense quark matter

Authors: Alexander Haber, Andreas Schmitt

Abstract: Color-flavor locked (CFL) quark matter expels color-magnetic fields due to the Meissner effect. One of these fields carries an admixture of the ordinary abelian magnetic field and therefore flux tubes may form if CFL matter is exposed to a magnetic field, possibly in the interior of neutron stars or in quark stars. We employ a Ginzburg-Landau approach for three massless quark flavors, which takes… ▽ More Color-flavor locked (CFL) quark matter expels color-magnetic fields due to the Meissner effect. One of these fields carries an admixture of the ordinary abelian magnetic field and therefore flux tubes may form if CFL matter is exposed to a magnetic field, possibly in the interior of neutron stars or in quark stars. We employ a Ginzburg-Landau approach for three massless quark flavors, which takes into account the multi-component nature of color superconductivity. Based on the weak-coupling expressions for the Ginzburg-Landau parameters, we identify the regime where CFL is a type-II color superconductor and compute the radial profiles of different color-magnetic flux tubes. Among the configurations without baryon circulation we find a new solution that is energetically preferred over the flux tubes previously discussed in the literature in the parameter regime relevant for compact stars. Within the same setup, we also find a new defect in the 2SC phase, namely magnetic domain walls, which emerge naturally from the previously studied flux tubes if a more general ansatz for the order parameter is used. Color-magnetic defects in the interior of compact stars allow for sustained deformations of the star, potentially strong enough to produce detectable gravitational waves. △ Less

Submitted 6 August, 2020; v1 submitted 22 December, 2017; originally announced December 2017.

Comments: 29 pages, 5 figures, v2: small modifications in the text, version accepted for publication in Journal of Physics G, v3: sign error in Sec. V in front of the charge $\tilde{q}_{83}$ corrected (all results unaffected since error was exactly compensated by negative winding number $n_3$, which is positive in the new version)

Reaction rates and transport in neutron stars

Authors: Andreas Schmitt, Peter Shternin

Abstract: Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions. Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions. △ Less

Submitted 29 October, 2018; v1 submitted 17 November, 2017; originally announced November 2017.

Comments: 74 pages; commissioned for the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes, references updated, overview graphic added in the introduction, improvements in Sec IV.A.4

Critical magnetic fields in a superconductor coupled to a superfluid

Authors: Alexander Haber, Andreas Schmitt

Abstract: We study a superconductor that is coupled to a superfluid via density and derivative couplings. Starting from a Lagrangian for two complex scalar fields, we derive a temperature-dependent Ginzburg-Landau potential, which is then used to compute the phase diagram at nonzero temperature and external magnetic field. This includes the calculation of the critical magnetic fields for the transition to a… ▽ More We study a superconductor that is coupled to a superfluid via density and derivative couplings. Starting from a Lagrangian for two complex scalar fields, we derive a temperature-dependent Ginzburg-Landau potential, which is then used to compute the phase diagram at nonzero temperature and external magnetic field. This includes the calculation of the critical magnetic fields for the transition to an array of magnetic flux tubes, based on an approximation for the interaction between the flux tubes. We find that the transition region between type-I and type-II superconductivity changes qualitatively due to the presence of the superfluid: the phase transitions at the upper and lower critical fields in the type-II regime become first order, opening the possibility of clustered flux tube phases. These flux tube clusters may be realized in the core of neutron stars, where superconducting protons are expected to be coupled to superfluid neutrons. △ Less

Submitted 19 June, 2017; v1 submitted 5 April, 2017; originally announced April 2017.

Comments: 29 pages, 7 figures; v2: references and clarifications added, version to appear in Phys. Rev. D

Journal ref: Phys. Rev. D 95, 116016 (2017)

Mixing of charged and neutral Bose condensates at nonzero temperature and magnetic field

Authors: Alexander Haber, Andreas Schmitt

Abstract: It is expected that in the interior of compact stars a proton superconductor coexists with and couples to a neutron superfluid. Starting from a field-theoretical model for two complex scalar fields - one of which is electrically charged - we derive a Ginzburg-Landau potential which includes entrainment between the two fluids and temperature effects from thermal excitations of the two scalar fields… ▽ More It is expected that in the interior of compact stars a proton superconductor coexists with and couples to a neutron superfluid. Starting from a field-theoretical model for two complex scalar fields - one of which is electrically charged - we derive a Ginzburg-Landau potential which includes entrainment between the two fluids and temperature effects from thermal excitations of the two scalar fields and the gauge field. The Ginzburg-Landau description is then used for an analysis of the phase structure in the presence of an external magnetic field. In particular, we study the effect of the superfluid on the flux tube phase by computing the various critical magnetic fields and deriving an approximation for the flux tube interaction. As a result, we point out differences to the naive expectations from an isolated superconductor, for instance the existence of a first-order flux tube onset, resulting in a more complicated phase structure in the region between type-I and type-II superconductivity. △ Less

Submitted 7 April, 2017; v1 submitted 5 December, 2016; originally announced December 2016.

Comments: 11 pages, contribution to the proceedings of "Quark Confinement and the Hadron Spectrum XII", Aug 28 - Sep 4, 2016, in Thessaloniki, Greece; v2: small corrections in Eqs. (9) and (13), references added

Phases of dense matter with holographic instantons

Authors: Florian Preis, Andreas Schmitt

Abstract: We discuss nuclear matter and the transition to quark matter in the decompactified limit of the Sakai-Sugimoto model. Nuclear matter is included through instantons on the flavor branes of the model. Our approximation is based on the flat-space solution, but we allow for a dynamical instanton width and deformation and compute the energetically preferred number of instanton layers in the bulk as a f… ▽ More We discuss nuclear matter and the transition to quark matter in the decompactified limit of the Sakai-Sugimoto model. Nuclear matter is included through instantons on the flavor branes of the model. Our approximation is based on the flat-space solution, but we allow for a dynamical instanton width and deformation and compute the energetically preferred number of instanton layers in the bulk as a function of the baryon chemical potential. We determine the regions in parameter space where the binding energy of nuclear matter is like in QCD, and compute the phase diagram in the plane of temperature and chemical potential. △ Less

Submitted 16 November, 2016; originally announced November 2016.

Comments: 9 pages, contribution to the proceedings of "XIIth Quark Confinement and the Hadron Spectrum" in Thessaloniki, Greece, Aug 28 - Sep 4, 2016

Layers of deformed instantons in holographic baryonic matter

Authors: Florian Preis, Andreas Schmitt

Abstract: We discuss homogeneous baryonic matter in the decompactified limit of the Sakai-Sugimoto model, improving existing approximations based on flat-space instantons. We allow for an anisotropic deformation of the instantons in the holographic and spatial directions and for a density-dependent distribution of arbitrarily many instanton layers in the bulk. Within our approximation, the baryon onset turn… ▽ More We discuss homogeneous baryonic matter in the decompactified limit of the Sakai-Sugimoto model, improving existing approximations based on flat-space instantons. We allow for an anisotropic deformation of the instantons in the holographic and spatial directions and for a density-dependent distribution of arbitrarily many instanton layers in the bulk. Within our approximation, the baryon onset turns out to be a second-order phase transition, at odds with nature, and there is no transition to quark matter at high densities, at odds with expectations from QCD. This changes when we impose certain constraints on the shape of single instantons, motivated by known features of holographic baryons in the vacuum. Then, a first-order baryon onset and chiral restoration at high density are possible, and at sufficiently large densities two instanton layers are formed dynamically. Our results are a further step towards describing realistic, strongly interacting matter over a large density regime within a single model, desirable for studies of compact stars. △ Less

Submitted 4 July, 2016; v1 submitted 2 June, 2016; originally announced June 2016.

Comments: 37 pages, 7 figures, v2: two panels added to fig. 5, version to appear in JHEP

Journal ref: J. High Energ. Phys. (2016) 2016

Instabilities in relativistic two-component (super)fluids

Authors: Alexander Haber, Andreas Schmitt, Stephan Stetina

Abstract: We study two-fluid systems with nonzero fluid velocities and compute their sound modes, which indicate various instabilities. For the case of two zero-temperature superfluids we employ a microscopic field-theoretical model of two coupled bosonic fields, including an entrainment coupling and a non-entrainment coupling. We analyse the onset of the various instabilities systematically and point out t… ▽ More We study two-fluid systems with nonzero fluid velocities and compute their sound modes, which indicate various instabilities. For the case of two zero-temperature superfluids we employ a microscopic field-theoretical model of two coupled bosonic fields, including an entrainment coupling and a non-entrainment coupling. We analyse the onset of the various instabilities systematically and point out that the dynamical two-stream instability can only occur beyond Landau's critical velocity, i.e., in an already energetically unstable regime. A qualitative difference is found for the case of two normal fluids, where certain transverse modes suffer a two-stream instability in an energetically stable regime if there is entrainment between the fluids. Since we work in a fully relativistic setup, our results are very general and of potential relevance for (super)fluids in neutron stars and, in the non-relativistic limit of our results, in the laboratory. △ Less

Submitted 25 January, 2016; v1 submitted 7 October, 2015; originally announced October 2015.

Comments: 25 pages, 7 figures, v2: minor modifications; references added; parts of Sec III.B moved into new appendix B; version published in Phys. Rev. D

Journal ref: Phys. Rev. D 93, 025011 (2016)

From holography towards real-world nuclear matter

Authors: Si-wen Li, Andreas Schmitt, Qun Wang

Abstract: Quantum chromodynamics is notoriously difficult to solve at nonzero baryon density, and most models or effective theories of dense quark or nuclear matter are restricted to a particular density regime and/or a particular form of matter. Here we study dense (and mostly cold) matter within the holographic Sakai-Sugimoto model, aiming at a strong-coupling framework in the wide density range between n… ▽ More Quantum chromodynamics is notoriously difficult to solve at nonzero baryon density, and most models or effective theories of dense quark or nuclear matter are restricted to a particular density regime and/or a particular form of matter. Here we study dense (and mostly cold) matter within the holographic Sakai-Sugimoto model, aiming at a strong-coupling framework in the wide density range between nuclear saturation density and ultra-high quark matter densities. The model contains only three parameters, and we ask whether it fulfills two basic requirements of real-world cold and dense matter, a first-order onset of nuclear matter and a chiral phase transition at high density to quark matter. Such a model would be extremely useful for astrophysical applications because it would provide a single equation of state for all densities relevant in a compact star. Our calculations are based on two approximations for baryonic matter, firstly an instanton gas and secondly a homogeneous ansatz for the non-abelian gauge fields on the flavor branes of the model. While the instanton gas shows chiral restoration at high densities but an unrealistic second-order baryon onset, the homogeneous ansatz behaves exactly the other way around. Our study thus provides all ingredients that are necessary for a more realistic model and allows for systematic improvements of the applied approximations. △ Less

Submitted 16 July, 2015; v1 submitted 19 May, 2015; originally announced May 2015.

Comments: 31 pages, 7 figures, v2: references added, version to appear in Physical Review D

Baryon onset in a magnetic field

Authors: Alexander Haber, Florian Preis, Andreas Schmitt

Abstract: The critical baryon chemical potential for the onset of nuclear matter is a function of the vacuum mass and the binding energy. Both quantities are affected by an external magnetic field. We show within two relativistic mean-field models - including magnetic catalysis, but omitting the anomalous magnetic moment - that a magnetic field increases both the vacuum mass and the binding energy. For suff… ▽ More The critical baryon chemical potential for the onset of nuclear matter is a function of the vacuum mass and the binding energy. Both quantities are affected by an external magnetic field. We show within two relativistic mean-field models - including magnetic catalysis, but omitting the anomalous magnetic moment - that a magnetic field increases both the vacuum mass and the binding energy. For sufficiently large magnetic fields, the effect on the vacuum mass dominates and as a result the critical baryon chemical potential is increased. △ Less

Submitted 19 December, 2014; originally announced December 2014.

Comments: 5 pages, 3 figures, to appear in the proceedings of "Quark Confinement and the Hadron Spectrum XI", St Petersburg, September 8-12, 2014

Magnetic catalysis in nuclear matter

Authors: Alexander Haber, Florian Preis, Andreas Schmitt

Abstract: A strong magnetic field enhances the chiral condensate at low temperatures. This so-called magnetic catalysis thus seeks to increase the vacuum mass of nucleons. We employ two relativistic field-theoretical models for nuclear matter, the Walecka model and an extended linear sigma model, to discuss the resulting effect on the transition between vacuum and nuclear matter at zero temperature. In both… ▽ More A strong magnetic field enhances the chiral condensate at low temperatures. This so-called magnetic catalysis thus seeks to increase the vacuum mass of nucleons. We employ two relativistic field-theoretical models for nuclear matter, the Walecka model and an extended linear sigma model, to discuss the resulting effect on the transition between vacuum and nuclear matter at zero temperature. In both models we find that the creation of nuclear matter in a sufficiently strong magnetic field becomes energetically more costly due to the heaviness of magnetized nucleons, even though it is also found that nuclear matter is more strongly bound in a magnetic field. Our results are potentially important for dense nuclear matter in compact stars, especially since previous studies in the astrophysical context have always ignored the contribution of the magnetized Dirac sea and thus the effect of magnetic catalysis. △ Less

Submitted 10 December, 2014; v1 submitted 1 September, 2014; originally announced September 2014.

Comments: 19 pages, 5 figures, v3: version to appear in Phys. Rev. D

Journal ref: Phys. Rev. D 90, 125036 (2014)

QCD and strongly coupled gauge theories: challenges and perspectives

Authors: N. Brambilla, S. Eidelman, P. Foka, S. Gardner, A. S. Kronfeld, M. G. Alford, R. Alkofer, M. Butenschoen, T. D. Cohen, J. Erdmenger, L. Fabbietti, M. Faber, J. L. Goity, B. Ketzer, H. W. Lin, F. J. Llanes-Estrada, H. Meyer, P. Pakhlov, E. Pallante, M. I. Polikarpov, H. Sazdjian, A. Schmitt, W. M. Snow, A. Vairo, R. Vogt , et al. (24 additional authors not shown)

Abstract: We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standar… ▽ More We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments. △ Less

Submitted 18 May, 2014; v1 submitted 14 April, 2014; originally announced April 2014.

Comments: 246 pp, around 128 figures; v2 adds material, references, and corrections suggested by readers of v1 -- to be submitted to EPJC

Report number: CCQCN-2014-24, CCTP-2014-5, CERN-PH-TH/2014-033, DF-1-2014, FERMILAB-PUB-14-024/T, HIP-2014-03/TH, ITEP-LAT-2014-1, JLAB-THY-14-1865, LLNL-JRNL-651216, MITP/14-016, NT@UW 14-04, RUB-TPII-01/2014, TUM-EFT 46/14, UWThPh-2014-006

Journal ref: Eur. Phys. J. C 74:2981 (2014) 1

Introduction to superfluidity -- Field-theoretical approach and applications

Authors: Andreas Schmitt

Abstract: In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also discuss various applications in low-energy and high-energy physics. Besides some introductory and standard topics such as superfluid helium and superfluidity in a sim… ▽ More In this pedagogical introduction, I discuss theoretical aspects of superfluidity and superconductivity, mostly using a field-theoretical formalism. While the emphasis is on general concepts and mechanisms behind superfluidity, I also discuss various applications in low-energy and high-energy physics. Besides some introductory and standard topics such as superfluid helium and superfluidity in a simple scalar field theory, the lecture notes also include more advanced chapters, for instance discussions of the covariant two-fluid formalism and Cooper pairing with mismatched Fermi surfaces. △ Less

Submitted 31 July, 2014; v1 submitted 4 April, 2014; originally announced April 2014.

Comments: 150 pages, v2: minor corrections, typos fixed, references added, version published in Lect. Notes Phys. 888, 1-155 (2014), ISBN 978-3-319-07946-2

Superfluid two-stream instability in a microscopic model

Authors: Andreas Schmitt

Abstract: The superflow in a superfluid is bounded from above by Landau's critical velocity. Within a microscopic bosonic model, I show that below this critical velocity there is a dynamical instability that manifests itself in an imaginary sound velocity and that is reminiscent of the two-stream instability in electromagnetic plasmas. I compute the onset of this instability and its full angular structure i… ▽ More The superflow in a superfluid is bounded from above by Landau's critical velocity. Within a microscopic bosonic model, I show that below this critical velocity there is a dynamical instability that manifests itself in an imaginary sound velocity and that is reminiscent of the two-stream instability in electromagnetic plasmas. I compute the onset of this instability and its full angular structure in a relativistic, uniform superfluid for all temperatures. At weak coupling, the instability only operates in a very small region in the phase diagram of temperature and superflow. Varying the coupling of the model suggests that the effect is more prominent at strong coupling and thus could be important for superfluids in compact stars and in the laboratory. △ Less

Submitted 3 March, 2014; v1 submitted 20 December, 2013; originally announced December 2013.

Comments: 14 pages, 9 figures, v2: small modifications in the text, version to appear in Phys. Rev. D

Journal ref: Phys. Rev. D 89, 065024 (2014)

Role reversal in first and second sound in a relativistic superfluid

Authors: Mark G. Alford, S. Kumar Mallavarapu, Andreas Schmitt, Stephan Stetina

Abstract: Relativistic superfluidity at arbitrary temperature, chemical potential and (uniform) superflow is discussed within a self-consistent field-theoretical approach. Our starting point is a complex scalar field with a $\varphi^4$ interaction, for which we calculate the 2-particle-irreducible effective action in the Hartree approximation. With this underlying microscopic theory, we can obtain the two-f… ▽ More Relativistic superfluidity at arbitrary temperature, chemical potential and (uniform) superflow is discussed within a self-consistent field-theoretical approach. Our starting point is a complex scalar field with a $\varphi^4$ interaction, for which we calculate the 2-particle-irreducible effective action in the Hartree approximation. With this underlying microscopic theory, we can obtain the two-fluid picture of a superfluid, and compute properties such as the superfluid density and the entrainment coefficient for all temperatures below the critical temperature for superfluidity. We compute the critical velocity, taking into account the full self-consistent effect of the temperature and superflow on the quasiparticle dispersion. We also discuss first and second sound modes and how first (second) sound evolves from a density (temperature) wave at low temperatures to a temperature (density) wave at high temperatures. This role reversal is investigated for ultra-relativistic and near-non-relativistic systems for zero and nonzero superflow. For nonzero superflow, we also observe a role reversal as a function of the direction of the sound wave. △ Less

Submitted 18 March, 2014; v1 submitted 22 October, 2013; originally announced October 2013.

Comments: 32 pages, 9 figures, v2: expanded discussion of renormalization, conclusions unchanged, version to appear in Phys. Rev. D

Journal ref: Phys. Rev. D 89, 085005 (2014)

From field theory to superfluid hydrodynamics of dense quark matter

Authors: Mark G. Alford, S. Kumar Mallavarapu, Andreas Schmitt, Stephan Stetina

Abstract: Hydrodynamics of superfluids can be described by formally dividing the fluid into a normal fluid and a superfluid part. In color-flavor locked quark matter, at least one superfluid component is present due to spontaneous breaking of baryon number conservation, and an additional one due to the breaking of strangeness arises once one takes into account kaon condensation. We show how such a two-compo… ▽ More Hydrodynamics of superfluids can be described by formally dividing the fluid into a normal fluid and a superfluid part. In color-flavor locked quark matter, at least one superfluid component is present due to spontaneous breaking of baryon number conservation, and an additional one due to the breaking of strangeness arises once one takes into account kaon condensation. We show how such a two-component description emerges from an underlying scalar field theory which can be viewed as an effective theory for kaons. Furthermore, the occurring hydrodynamic quantities in the low-temperature limit are related to the microscopic parameters provided by the Lagrangian which closes the gap between field theory and hydrodynamics, which are important for astrophysical calculations. △ Less

Submitted 23 July, 2013; v1 submitted 26 April, 2013; originally announced April 2013.

Comments: 8 pages, 1 figure; v2: version to appear in the Conference Proceedings of "Compact Stars in the QCD Phase Diagram III (CSQCD III)", December 12-15, 2012, Guarujá, Brazil. http://www.astro.iag.usp.br/~foton/CSQCD3

Relativistic superfluid hydrodynamics from field theory

Authors: Mark G. Alford, S. Kumar Mallavarapu, Andreas Schmitt, Stephan Stetina

Abstract: It is well known that the hydrodynamics of a zero-temperature superfluid can be formulated in field-theoretic terms, relating for example the superfluid four-velocity to the gradient of the phase of a Bose-condensed scalar field. At nonzero temperatures, where the phenomenology of a superfluid is usually described within a two-fluid picture, this relationship is less obvious. For the case of a uni… ▽ More It is well known that the hydrodynamics of a zero-temperature superfluid can be formulated in field-theoretic terms, relating for example the superfluid four-velocity to the gradient of the phase of a Bose-condensed scalar field. At nonzero temperatures, where the phenomenology of a superfluid is usually described within a two-fluid picture, this relationship is less obvious. For the case of a uniform, dissipationless superfluid at small temperatures and weak coupling we discuss this relationship within a phi^4 model. For instance, we compute the entrainment coefficient, which describes the interaction between the superfluid and the normal-fluid components, and the velocities of first and second sound in the presence of a superflow. Our study is very general, but can also be seen as a step towards understanding the superfluid properties of various phases of dense nuclear and quark matter in the interior of compact stars. △ Less

Submitted 18 December, 2012; originally announced December 2012.

Comments: 8 pages, 1 figure, contribution to the proceedings of "Xth Quark Confinement and the Hadron Spectrum", October 8-12, 2012, Munich, Germany

From a complex scalar field to the two-fluid picture of superfluidity

Authors: Mark G. Alford, S. Kumar Mallavarapu, Andreas Schmitt, Stephan Stetina

Abstract: The hydrodynamic description of a superfluid is usually based on a two-fluid picture. We compute the basic properties of the relativistic two-fluid system from the underlying microscopic physics of a relativistic \varphi^4 complex scalar field theory. We work at nonzero but small temperature and weak coupling, and we neglect dissipation. We clarify the relationship between different formulations o… ▽ More The hydrodynamic description of a superfluid is usually based on a two-fluid picture. We compute the basic properties of the relativistic two-fluid system from the underlying microscopic physics of a relativistic \varphi^4 complex scalar field theory. We work at nonzero but small temperature and weak coupling, and we neglect dissipation. We clarify the relationship between different formulations of the two-fluid model, and how they are parameterized in terms of partly redundant current and momentum 4-vectors. As an application, we compute the velocities of first and second sound at small temperatures and in the presence of a superflow. While our results are of a very general nature, we also comment on their interpretation as a step towards the hydrodynamics of the color-flavor locked state of quark matter, which, in particular in the presence of kaon condensation, appears to be a complicated multi-component fluid. △ Less

Submitted 25 July, 2013; v1 submitted 4 December, 2012; originally announced December 2012.

Comments: 22 + 6 pages, 1 figure; v3: typos in Eqs. (5a) and (84) corrected

"Strongly interacting matter in magnetic fields": an overview

Authors: Dmitri E. Kharzeev, Karl Landsteiner, Andreas Schmitt, Ho-Ung Yee

Abstract: This is an introduction to the volume of Lecture Notes in Physics on "Strongly interacting matter in magnetic fields". The volume combines contributions written by a number of experts on different aspects of the problem. The response of QCD matter to intense magnetic fields has attracted a lot of interest recently. On the theoretical side, this interest stems from the possibility to explore the pl… ▽ More This is an introduction to the volume of Lecture Notes in Physics on "Strongly interacting matter in magnetic fields". The volume combines contributions written by a number of experts on different aspects of the problem. The response of QCD matter to intense magnetic fields has attracted a lot of interest recently. On the theoretical side, this interest stems from the possibility to explore the plethora of novel phenomena arising from the interplay of magnetic field with QCD dynamics. On the experimental side, the interest is motivated by the recent results on the behavior of quark-gluon plasma in a strong magnetic field created in relativistic heavy ion collisions at RHIC and LHC. The purpose of this introduction is to provide a brief overview and a guide to the individual contributions where these topics are covered in detail. △ Less

Submitted 27 May, 2013; v1 submitted 27 November, 2012; originally announced November 2012.

Comments: 12 pages, introduction to "Strongly interacting matter in magnetic fields", Lect. Notes Phys. 871, 1 (2013), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee; v2: references updated

Chiral transition in dense, magnetized matter

Authors: Florian Preis, Anton Rebhan, Andreas Schmitt

Abstract: In the presence of a chemical potential, the effect of a magnetic field on chiral symmetry breaking goes beyond the well-known magnetic catalysis. Due to a subtle interplay with the chemical potential, the magnetic field may work not only in favor but also against the chirally broken phase. At sufficiently large coupling, the magnetic field favors the broken phase only for field strengths beyond a… ▽ More In the presence of a chemical potential, the effect of a magnetic field on chiral symmetry breaking goes beyond the well-known magnetic catalysis. Due to a subtle interplay with the chemical potential, the magnetic field may work not only in favor but also against the chirally broken phase. At sufficiently large coupling, the magnetic field favors the broken phase only for field strengths beyond any conceivable value in nature. Therefore, in the interior of magnetars, a possible transition from chirally broken hadronic matter to chirally symmetric quark matter might occur at smaller densities than previously thought. △ Less

Submitted 20 September, 2012; originally announced September 2012.

Comments: 5 pages, 2 figures, contribution to proceedings of "QCD@Work 2012", Lecce, Italy

Inverse magnetic catalysis in field theory and gauge-gravity duality

Authors: Florian Preis, Anton Rebhan, Andreas Schmitt

Abstract: We investigate the surface of the chiral phase transition in the three-dimensional parameter space of temperature, baryon chemical potential and magnetic field in two different approaches, the field-theoretical Nambu-Jona-Lasinio (NJL) model and the holographic Sakai-Sugimoto model. The latter is a top-down approach to a gravity dual of QCD with an asymptotically large number of colors and becomes… ▽ More We investigate the surface of the chiral phase transition in the three-dimensional parameter space of temperature, baryon chemical potential and magnetic field in two different approaches, the field-theoretical Nambu-Jona-Lasinio (NJL) model and the holographic Sakai-Sugimoto model. The latter is a top-down approach to a gravity dual of QCD with an asymptotically large number of colors and becomes, in a certain limit, dual to an NJL-like model. Our main observation is that, at nonzero chemical potential, a magnetic field can restore chiral symmetry, in apparent contrast to the phenomenon of magnetic catalysis. This "inverse magnetic catalysis" occurs in the Sakai-Sugimoto model and, for sufficiently large coupling, in the NJL model and is related to the physics of the lowest Landau level. While in most parts our discussion is a pedagogical review of previously published results, we include new analytical results for the NJL approach and a thorough comparison of inverse magnetic catalysis in the two approaches. △ Less

Submitted 2 August, 2012; originally announced August 2012.

Comments: 37 pages, 11 figures, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Yee

Holographic baryonic matter in a background magnetic field

Authors: Florian Preis, Anton Rebhan, Andreas Schmitt

Abstract: We discuss the effect of baryonic matter on the zero-temperature chiral phase transition at finite chemical potential in the presence of a background magnetic field. The main part of our study is done in the deconfined geometry of the Sakai-Sugimoto model, i.e., at large N_c and strong coupling, with non-antipodal separation of the flavor branes. We find that for not too large magnetic fields bary… ▽ More We discuss the effect of baryonic matter on the zero-temperature chiral phase transition at finite chemical potential in the presence of a background magnetic field. The main part of our study is done in the deconfined geometry of the Sakai-Sugimoto model, i.e., at large N_c and strong coupling, with non-antipodal separation of the flavor branes. We find that for not too large magnetic fields baryonic matter completely removes the chiral phase transition: chirally broken matter persists up to arbitrarily large chemical potential. At sufficiently large magnetic fields, baryonic matter becomes disfavored and mesonic matter is directly superseded by quark matter. In order to discuss the possible relevance of our results to QCD, we compute the baryon onset in a relativistic mean-field model including the anomalous magnetic moment and point out the differences to our holographic calculation. △ Less

Submitted 23 March, 2012; v1 submitted 30 September, 2011; originally announced September 2011.

Comments: 29 pages, 8 figures, v2: references added, minor reformulations in the text, version accepted for publication in Journal of Physics G

Inverse magnetic catalysis in dense holographic matter

Authors: Florian Preis, Anton Rebhan, Andreas Schmitt

Abstract: We study the chiral phase transition in a magnetic field at finite temperature and chemical potential within the Sakai-Sugimoto model, a holographic top-down approach to (large-N_c) QCD. We consider the limit of a small separation of the flavor D8-branes, which corresponds to a dual field theory comparable to a Nambu-Jona Lasinio (NJL) model. Mapping out the surface of the chiral phase transition… ▽ More We study the chiral phase transition in a magnetic field at finite temperature and chemical potential within the Sakai-Sugimoto model, a holographic top-down approach to (large-N_c) QCD. We consider the limit of a small separation of the flavor D8-branes, which corresponds to a dual field theory comparable to a Nambu-Jona Lasinio (NJL) model. Mapping out the surface of the chiral phase transition in the parameter space of magnetic field strength, quark chemical potential, and temperature, we find that for small temperatures the addition of a magnetic field decreases the critical chemical potential for chiral symmetry restoration - in contrast to the case of vanishing chemical potential where, in accordance with the familiar phenomenon of magnetic catalysis, the magnetic field favors the chirally broken phase. This "inverse magnetic catalysis" (IMC) appears to be associated with a previously found magnetic phase transition within the chirally symmetric phase that shows an intriguing similarity to a transition into the lowest Landau level. We estimate IMC to persist up to 10^{19} G at low temperatures. △ Less

Submitted 16 February, 2011; v1 submitted 21 December, 2010; originally announced December 2010.

Comments: 42 pages, 11 figures, v3: extended discussion; new appendix D; references added; version to appear in JHEP

Journal ref: JHEP 1103:033,2011

Ginzburg-Landau phase diagram for dense matter with axial anomaly, strange quark mass, and meson condensation

Authors: Andreas Schmitt, Stephan Stetina, Motoi Tachibana

Abstract: We discuss the phase structure of dense matter, in particular the nature of the transition between hadronic and quark matter. Calculations within a Ginzburg-Landau approach show that the axial anomaly can induce a critical point in this transition region. This is possible because in three-flavor quark matter with instanton effects a chiral condensate can be added to the color-flavor locked (CFL) p… ▽ More We discuss the phase structure of dense matter, in particular the nature of the transition between hadronic and quark matter. Calculations within a Ginzburg-Landau approach show that the axial anomaly can induce a critical point in this transition region. This is possible because in three-flavor quark matter with instanton effects a chiral condensate can be added to the color-flavor locked (CFL) phase without changing the symmetries of the ground state. In (massless) two-flavor quark matter such a critical point is not possible since the corresponding color superconductor (2SC) does not break chiral symmetry. We study the effects of a nonzero but finite strange quark mass which interpolates between these two cases. Since at ultra-high density the first reaction of CFL to a nonzero strange quark mass is to develop a kaon condensate, we extend previous Ginzburg-Landau studies by including such a condensate. We discuss the fate of the critical point systematically and show that the continuity between hadronic and quark matter can be disrupted by the onset of a kaon condensate. Moreover, we identify the mass terms in the Ginzburg-Landau potential which are needed for the 2SC phase to occur in the phase diagram. △ Less

Submitted 1 February, 2011; v1 submitted 20 October, 2010; originally announced October 2010.

Comments: 25 pages, 10 figures, v2: small modifications; references added; version to appear in Phys.Rev.D

Journal ref: Phys.Rev.D83:045008,2011

Holographic chiral currents in a magnetic field

Authors: Anton Rebhan, Andreas Schmitt, Stefan Stricker

Abstract: In the presence of a quark chemical potential, a magnetic field induces an axial current in the direction of the magnetic field. We compute this current in the Sakai-Sugimoto model, a holographic model which, in a certain limit, is dual to large-N_c QCD. We also compute the analogous vector current, for which an axial chemical potential is formally introduced. This vector current can potentially b… ▽ More In the presence of a quark chemical potential, a magnetic field induces an axial current in the direction of the magnetic field. We compute this current in the Sakai-Sugimoto model, a holographic model which, in a certain limit, is dual to large-N_c QCD. We also compute the analogous vector current, for which an axial chemical potential is formally introduced. This vector current can potentially be observed via charge separation in heavy-ion collisions. After implementing the correct axial anomaly in the Sakai-Sugimoto model we find an axial current in accordance with previous studies and a vanishing vector current, in apparent contrast to previous weak-coupling calculations. △ Less

Submitted 15 July, 2010; originally announced July 2010.

Comments: 8 pages, to appear in the proceedings of "New Frontiers in QCD 2010", Yukawa Institute for Theoretical Physics, Kyoto, Japan, Jan 18 - Mar 19, 2010

Journal ref: Prog.Theor.Phys.Suppl.186:463-470,2010

Dense matter in compact stars - A pedagogical introduction

Authors: Andreas Schmitt

Abstract: Cold and dense nuclear and/or quark matter can be found in the interior of compact stars. It is very challenging to determine the ground state and properties of this matter because of the strong-coupling nature of QCD. I give a pedagogical introduction to microscopic calculations based on phenomenological models, effective theories, and perturbative QCD. I discuss how the results of these calculat… ▽ More Cold and dense nuclear and/or quark matter can be found in the interior of compact stars. It is very challenging to determine the ground state and properties of this matter because of the strong-coupling nature of QCD. I give a pedagogical introduction to microscopic calculations based on phenomenological models, effective theories, and perturbative QCD. I discuss how the results of these calculations can be related to astrophysical observations to potentially rule out or confirm candidate phases of dense matter. △ Less

Submitted 25 June, 2010; v1 submitted 19 January, 2010; originally announced January 2010.

Comments: 138+10 pages, v2: small modifications, typos fixed, Figs. 2.1 and 3.7 slightly changed; to appear in Lect. Notes Phys. (Springer), ISBN 978-3-642-12865-3

Journal ref: Lect.Notes Phys.811:1-111,2010

Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model

Authors: Anton Rebhan, Andreas Schmitt, Stefan A. Stricker

Abstract: In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED… ▽ More In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED anomaly. In the Sakai-Sugimoto model, which in a certain limit is dual to large-N_c QCD, we discuss the proper implementation of the QED axial anomaly, the (ambiguous) definition of chiral currents, and the calculation of the chiral magnetic effect. We show that this model correctly contains the so-called consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly. Introducing net chirality through an axial chemical potential, we find a nonvanishing vector current only before including this counterterm. This seems to imply the absence of the chiral magnetic effect in this model. On the other hand, for a conventional quark chemical potential and large magnetic field, which is of interest in the physics of compact stars, we obtain a nontrivial result for the axial current that is in agreement with previous calculations and known exact results for QCD. △ Less

Submitted 15 December, 2009; v1 submitted 28 September, 2009; originally announced September 2009.

Comments: 35 pages, 4 figures, v2: added comments about frequency-dependent conductivity at the end of section 4; references added; version to appear in JHEP

Journal ref: JHEP 1001:026,2010

One-loop results for kink and domain wall profiles at zero and finite temperature

Authors: Anton Rebhan, Andreas Schmitt, Peter van Nieuwenhuizen

Abstract: Using dimensional regularization, we compute the one-loop quantum and thermal corrections to the profile of the bosonic 1+1-dimensional phi^4 kink, the sine-Gordon kink and the CP^1 kink, and higher-dimensional phi^4 kink domain walls. Starting from the Heisenberg field equation in the presence of the nontrivial kink background we derive analytically results for the temperature-dependent mean fi… ▽ More Using dimensional regularization, we compute the one-loop quantum and thermal corrections to the profile of the bosonic 1+1-dimensional phi^4 kink, the sine-Gordon kink and the CP^1 kink, and higher-dimensional phi^4 kink domain walls. Starting from the Heisenberg field equation in the presence of the nontrivial kink background we derive analytically results for the temperature-dependent mean field which display the onset of the melting of kinks as the system is heated towards a symmetry restoring phase transition. The result is shown to simplify significantly when expressed in terms of a self-consistently defined thermal screening mass. In the case of domain walls, we find infrared singularities in the kink profile, which corresponds to interface roughening depending on the system size. Finally we calculate the energy density profile of phi^4 kink domain walls and find that in contrast to the total surface tension the local distribution requires composite operator renormalization in 3+1 dimensions. △ Less

Submitted 3 July, 2009; v1 submitted 30 March, 2009; originally announced March 2009.

Comments: REVTEX4 24 pages, 4 figures. v3: minor rewordings in abstract and introduction, consistency with previous results clarified, references added

Report number: TUW-09-02, YITP-SB-09-03

Journal ref: Phys.Rev.D80:045012,2009

Meson supercurrents and the Meissner effect in the Sakai-Sugimoto model

Authors: Anton Rebhan, Andreas Schmitt, Stefan A. Stricker

Abstract: The Sakai-Sugimoto model provides a holographic description for chiral symmetry breaking. We use this model to investigate chirally broken phases in an external magnetic field at finite isospin and baryon chemical potentials. The equations of motion for the bulk gauge fields are solved analytically and the free energy is computed from the Yang-Mills and Chern-Simons contributions to the D8 brane… ▽ More The Sakai-Sugimoto model provides a holographic description for chiral symmetry breaking. We use this model to investigate chirally broken phases in an external magnetic field at finite isospin and baryon chemical potentials. The equations of motion for the bulk gauge fields are solved analytically and the free energy is computed from the Yang-Mills and Chern-Simons contributions to the D8 brane action. In the case of a neutral pion condensate, a magnetic field is found to induce nonzero gradients of the Goldstone boson fields corresponding to meson supercurrents. A charged pion condensate, on the other hand, expels the magnetic field due to the Meissner effect. Upon comparing the Gibbs free energies of these two phases we find that the rotation of the chiral condensate into a charged pion condensate for finite isospin chemical potentials is partially undone by switching on a magnetic field, and we determine the critical magnetic field which removes the charged pion condensate in a first-order phase transition. △ Less

Submitted 22 May, 2009; v1 submitted 21 November, 2008; originally announced November 2008.

Comments: 46 pages, 5 figures, v2: small modifications and added footnotes in discussion of axial current and number density (p19, p24); typos corrected; references added; version to appear in JHEP

Journal ref: JHEP 0905:084,2009