Abstract
We study semiclassical spiky strings in de Sitter space and the corresponding Regge trajectories, generalizing the analysis in anti-de Sitter space. In particular we demonstrate that each Regge trajectory has a maximum spin due to de Sitter acceleration, similarly to the folded string studied earlier. While this property is useful for the spectrum to satisfy the Higuchi bound, it makes a nontrivial question how to maintain mildness of high-energy string scattering which we are familiar with in flat space and anti-de Sitter space. Our analysis implies that in order to have infinitely many higher spin states, one needs to consider infinitely many Regge trajectories with an increasing folding number.
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U.H. Danielsson and T. Van Riet, What if string theory has no de Sitter vacua?, Int. J. Mod. Phys. D 27 (2018) 1830007 [arXiv:1804.01120] [INSPIRE].
J.M. Maldacena and C. Núñez, Supergravity description of field theories on curved manifolds and a no go theorem, Int. J. Mod. Phys. A 16 (2001) 822 [hep-th/0007018] [INSPIRE].
S. Kachru, R. Kallosh, A.D. Linde and S.P. Trivedi, de Sitter vacua in string theory, Phys. Rev. D 68 (2003) 046005 [hep-th/0301240] [INSPIRE].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
S.K. Garg and C. Krishnan, Bounds on Slow Roll and the de Sitter Swampland, JHEP 11 (2019) 075 [arXiv:1807.05193] [INSPIRE].
H. Ooguri, E. Palti, G. Shiu and C. Vafa, Distance and de Sitter Conjectures on the Swampland, Phys. Lett. B 788 (2019) 180 [arXiv:1810.05506] [INSPIRE].
T. Noumi, T. Takeuchi and S. Zhou, String Regge trajectory on de Sitter space and implications to inflation, Phys. Rev. D 102 (2020) 126012 [arXiv:1907.02535] [INSPIRE].
H.J. de Vega and N.G. Sanchez, A New Approach to String Quantization in Curved Space-Times, Phys. Lett. B 197 (1987) 320 [INSPIRE].
H.J. de Vega and N.G. Sanchez, Quantum Dynamics of Strings in Black Hole Space-times, Nucl. Phys. B 309 (1988) 552 [INSPIRE].
F. Combes, H.J. de Vega, A.V. Mikhailov and N.G. Sanchez, Multistring solutions by soliton methods in de Sitter space-time, Phys. Rev. D 50 (1994) 2754 [hep-th/9310073] [INSPIRE].
H.J. de Vega, A.L. Larsen and N.G. Sanchez, Semiclassical quantization of circular strings in de Sitter and anti-de Sitter space-times, Phys. Rev. D 51 (1995) 6917 [hep-th/9410219] [INSPIRE].
H.J. de Vega and I.L. Egusquiza, Planetoid string solutions in (3 + 1) axisymmetric space-times, Phys. Rev. D 54 (1996) 7513 [hep-th/9607056] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A Semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
A.A. Tseytlin, Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions, Lett. Math. Phys. 99 (2012) 103 [arXiv:1012.3986] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
S. Frolov and A.A. Tseytlin, Semiclassical quantization of rotating superstring in AdS5 × S5, JHEP 06 (2002) 007 [hep-th/0204226] [INSPIRE].
J.A. Minahan, Circular semiclassical string solutions on AdS5 × S5 , Nucl. Phys. B 648 (2003) 203 [hep-th/0209047] [INSPIRE].
S. Frolov and A.A. Tseytlin, Multispin string solutions in AdS5 × S5, Nucl. Phys. B 668 (2003) 77 [hep-th/0304255] [INSPIRE].
S. Frolov and A.A. Tseytlin, Rotating string solutions: AdS/CFT duality in nonsupersymmetric sectors, Phys. Lett. B 570 (2003) 96 [hep-th/0306143] [INSPIRE].
J. Engquist, J.A. Minahan and K. Zarembo, Yang-Mills duals for semiclassical strings on AdS5 × S5, JHEP 11 (2003) 063 [hep-th/0310188] [INSPIRE].
G. Arutyunov, J. Russo and A.A. Tseytlin, Spinning strings in AdS5 × S5: New integrable system relations, Phys. Rev. D 69 (2004) 086009 [hep-th/0311004] [INSPIRE].
A.L. Larsen and A. Khan, Novel explicit multispin string solitons in AdS5, Nucl. Phys. B 686 (2004) 75 [hep-th/0312184] [INSPIRE].
S. Ryang, Folded three spin string solutions in AdS5 × S5, JHEP 04 (2004) 053 [hep-th/0403180] [INSPIRE].
M. Kruczenski and A.A. Tseytlin, Semiclassical relativistic strings in S5 and long coherent operators in N = 4 SYM theory, JHEP 09 (2004) 038 [hep-th/0406189] [INSPIRE].
M. Kruczenski, Spiky strings and single trace operators in gauge theories, JHEP 08 (2005) 014 [hep-th/0410226] [INSPIRE].
S. Ryang, Wound and rotating strings in AdS5 × S5, JHEP 08 (2005) 047 [hep-th/0503239] [INSPIRE].
I.Y. Park, A. Tirziu and A.A. Tseytlin, Semiclassical circular strings in AdS5 and ‘long’ gauge field strength operators, Phys. Rev. D 71 (2005) 126008 [hep-th/0505130] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Giant Magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
N. Dorey, Magnon Bound States and the AdS/CFT Correspondence, J. Phys. A 39 (2006) 13119 [hep-th/0604175] [INSPIRE].
T. McLoughlin and X. Wu, Kinky Strings in AdS5 × S5, JHEP 08 (2006) 063 [hep-th/0604193] [INSPIRE].
H.-Y. Chen, N. Dorey and K. Okamura, Dyonic giant magnons, JHEP 09 (2006) 024 [hep-th/0605155] [INSPIRE].
G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size Effects from Giant Magnons, Nucl. Phys. B 778 (2007) 1 [hep-th/0606126] [INSPIRE].
J.A. Minahan, A. Tirziu and A.A. Tseytlin, Infinite spin limit of semiclassical string states, JHEP 08 (2006) 049 [hep-th/0606145] [INSPIRE].
M. Spradlin and A. Volovich, Dressing the Giant Magnon, JHEP 10 (2006) 012 [hep-th/0607009] [INSPIRE].
N.P. Bobev and R.C. Rashkov, Multispin Giant Magnons, Phys. Rev. D 74 (2006) 046011 [hep-th/0607018] [INSPIRE].
M. Kruczenski, J. Russo and A.A. Tseytlin, Spiky strings and giant magnons on S5, JHEP 10 (2006) 002 [hep-th/0607044] [INSPIRE].
K. Okamura and R. Suzuki, A Perspective on Classical Strings from Complex sine-Gordon Solitons, Phys. Rev. D 75 (2007) 046001 [hep-th/0609026] [INSPIRE].
S. Ryang, Three-spin giant magnons in AdS5 × S5, JHEP 12 (2006) 043 [hep-th/0610037] [INSPIRE].
R. Ishizeki and M. Kruczenski, Single spike solutions for strings on S2 and S3, Phys. Rev. D 76 (2007) 126006 [arXiv:0705.2429] [INSPIRE].
A.E. Mosaffa and B. Safarzadeh, Dual spikes: New spiky string solutions, JHEP 08 (2007) 017 [arXiv:0705.3131] [INSPIRE].
H. Hayashi, K. Okamura, R. Suzuki and B. Vicedo, Large Winding Sector of AdS/CFT, JHEP 11 (2007) 033 [arXiv:0709.4033] [INSPIRE].
R. Ishizeki, M. Kruczenski, M. Spradlin and A. Volovich, Scattering of single spikes, JHEP 02 (2008) 009 [arXiv:0710.2300] [INSPIRE].
A. Mikhailov and S. Schäfer-Nameki, sine-Gordon-like action for the Superstring in AdS5 × S5, JHEP 05 (2008) 075 [arXiv:0711.0195] [INSPIRE].
A. Jevicki, K. Jin, C. Kalousios and A. Volovich, Generating AdS String Solutions, JHEP 03 (2008) 032 [arXiv:0712.1193] [INSPIRE].
M. Kruczenski and A.A. Tseytlin, Spiky strings, light-like Wilson loops and pp-wave anomaly, Phys. Rev. D 77 (2008) 126005 [arXiv:0802.2039] [INSPIRE].
A. Jevicki and K. Jin, Solitons and AdS String Solutions, Int. J. Mod. Phys. A 23 (2008) 2289 [arXiv:0804.0412] [INSPIRE].
J.L. Miramontes, Pohlmeyer reduction revisited, JHEP 10 (2008) 087 [arXiv:0808.3365] [INSPIRE].
S. Ryang, Conformal SO(2, 4) Transformations for the Helical AdS String Solution, JHEP 05 (2008) 021 [arXiv:0803.3855] [INSPIRE].
M.C. Abbott and I.V. Aniceto, Vibrating giant spikes and the large-winding sector, JHEP 06 (2008) 088 [arXiv:0803.4222] [INSPIRE].
R. Ishizeki, M. Kruczenski, A. Tirziu and A.A. Tseytlin, Spiky strings in AdS3 × S1 and their AdS-pp-wave limits, Phys. Rev. D 79 (2009) 026006 [arXiv:0812.2431] [INSPIRE].
T.J. Hollowood and J.L. Miramontes, Magnons, their Solitonic Avatars and the Pohlmeyer Reduction, JHEP 04 (2009) 060 [arXiv:0902.2405] [INSPIRE].
A. Jevicki and K. Jin, Moduli Dynamics of AdS3 Strings, JHEP 06 (2009) 064 [arXiv:0903.3389] [INSPIRE].
A. Tirziu and A.A. Tseytlin, Semiclassical rigid strings with two spins in AdS5, Phys. Rev. D 81 (2010) 026006 [arXiv:0911.2417] [INSPIRE].
M. Kruczenski and A. Tirziu, Spiky strings in Bethe Ansatz at strong coupling, Phys. Rev. D 81 (2010) 106004 [arXiv:1002.4843] [INSPIRE].
K. Zarembo, Holographic three-point functions of semiclassical states, JHEP 09 (2010) 030 [arXiv:1008.1059] [INSPIRE].
M.S. Costa, R. Monteiro, J.E. Santos and D. Zoakos, On three-point correlation functions in the gauge/gravity duality, JHEP 11 (2010) 141 [arXiv:1008.1070] [INSPIRE].
R.A. Janik and A. Wereszczynski, Correlation functions of three heavy operators: The AdS contribution, JHEP 12 (2011) 095 [arXiv:1109.6262] [INSPIRE].
Y. Kazama and S. Komatsu, On holographic three point functions for GKP strings from integrability, JHEP 01 (2012) 110 [Erratum ibid. 06 (2012) 150] [arXiv:1110.3949] [INSPIRE].
J. Caetano and J. Toledo, χ-systems for correlation functions, JHEP 01 (2019) 050 [arXiv:1208.4548] [INSPIRE].
Y. Kazama and S. Komatsu, Three-point functions in the SU(2) sector at strong coupling, JHEP 03 (2014) 052 [arXiv:1312.3727] [INSPIRE].
Y. Kazama, S. Komatsu and T. Nishimura, Classical Integrability for Three-point Functions: Cognate Structure at Weak and Strong Couplings, JHEP 10 (2016) 042 [Erratum ibid. 02 (2018) 047] [arXiv:1603.03164] [INSPIRE].
A. Higuchi, Forbidden Mass Range for Spin-2 Field Theory in de Sitter Space-time, Nucl. Phys. B 282 (1987) 397 [INSPIRE].
D. Lüst and E. Palti, A Note on String Excitations and the Higuchi Bound, Phys. Lett. B 799 (2019) 135067 [arXiv:1907.04161] [INSPIRE].
H.J. de Vega, A.L. Larsen and N.G. Sanchez, Infinitely many strings in de Sitter space-time: Expanding and oscillating elliptic function solutions, Nucl. Phys. B 427 (1994) 643 [hep-th/9312115] [INSPIRE].
M. Gary, S.B. Giddings and J. Penedones, Local bulk S-matrix elements and CFT singularities, Phys. Rev. D 80 (2009) 085005 [arXiv:0903.4437] [INSPIRE].
T. Okuda and J. Penedones, String scattering in flat space and a scaling limit of Yang-Mills correlators, Phys. Rev. D 83 (2011) 086001 [arXiv:1002.2641] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
S. Raju, New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators, Phys. Rev. D 85 (2012) 126009 [arXiv:1201.6449] [INSPIRE].
M.S. Costa, V. Goncalves and J. Penedones, Conformal Regge theory, JHEP 12 (2012) 091 [arXiv:1209.4355] [INSPIRE].
J. Maldacena, D. Simmons-Duffin and A. Zhiboedov, Looking for a bulk point, JHEP 01 (2017) 013 [arXiv:1509.03612] [INSPIRE].
P. Haldar and A. Sinha, Froissart bound for/from CFT Mellin amplitudes, SciPost Phys. 8 (2020) 095 [arXiv:1911.05974] [INSPIRE].
D. Meltzer, AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering, JHEP 05 (2020) 133 [arXiv:1912.05580] [INSPIRE].
S. Komatsu, M.F. Paulos, B.C. Van Rees and X. Zhao, Landau diagrams in AdS and S-matrices from conformal correlators, JHEP 11 (2020) 046 [arXiv:2007.13745] [INSPIRE].
D. Chandorkar, S.D. Chowdhury, S. Kundu and S. Minwalla, Bounds on Regge growth of flat space scattering from bounds on chaos, arXiv:2102.03122 [INSPIRE].
N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
N. Arkani-Hamed, P. Benincasa and A. Postnikov, Cosmological Polytopes and the Wavefunction of the Universe, arXiv:1709.02813 [INSPIRE].
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Kato, M., Nishii, K., Noumi, T. et al. Spiky strings in de Sitter space. J. High Energ. Phys. 2021, 47 (2021). https://doi.org/10.1007/JHEP05(2021)047
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DOI: https://doi.org/10.1007/JHEP05(2021)047