Holographic thermal correlators for hyperbolic CFTs

Journal of High Energy Physics
Atanu Bhatta, Shankhadeep Chakrabortty, Taniya Mandal, Arpit Maurya

Tóm tắt

Abstract We use holography to compute the exact form of retarded Green’s functions for a scalar operator with conformal dimension ∆ in a thermal CFT and in its related counterpart with chemical potential in R1 × H3. In our analysis, we recast the wave equation of a scalar field in the normal form of Heun’s equation in the dual gravity theories described by the AdS hyperbolic blackhole and its charged version. Heun’s equation is identified to the semiclassical limit of the BPZ equation for a five-point correlator with one degenerate field insertion in the Liouville theory on the Riemann sphere. The crossing symmetry of conformal block in the Liouville theory eventually gives rise to a set of connection formulas among the solutions of Heun’s equation evaluated at different regular singularities. We use the connection formula to reproduce the leading order behaviors of the scalar field near the horizon as well as near the boundary and achieve the exact form of the retarded thermal Green’s function. We show a recipe to obtain the exact retarded Green’s function for a thermal CFT dual to AdS blackbrane from a high-temperature limit accompanied by a complex mapping on AdS hyperbolic blackhole. Moreover, we show the retarded Green’s function for the boundary CFT of Rindler AdS spacetime admits a free integer parameter.

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Tài liệu tham khảo

J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].

S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

J. Louko, D. Marolf and S.F. Ross, On geodesic propagators and black hole holography, Phys. Rev. D 62 (2000) 044041 [hep-th/0002111] [INSPIRE].

D. Rodriguez-Gomez and J.G. Russo, Thermal correlation functions in CFT and factorization, JHEP 11 (2021) 049 [arXiv:2105.13909] [INSPIRE].

D. Rodriguez-Gomez and J.G. Russo, Correlation functions in finite temperature CFT and black hole singularities, JHEP 06 (2021) 048 [arXiv:2102.11891] [INSPIRE].

G. Georgiou and D. Zoakos, Holographic correlation functions at finite density and/or finite temperature, JHEP 11 (2022) 087 [arXiv:2209.14661] [INSPIRE].

V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of anti-de Sitter space-times, Phys. Rev. D 59 (1999) 104021 [hep-th/9808017] [INSPIRE].

V. Balasubramanian, S.B. Giddings and A.E. Lawrence, What do CFTs tell us about anti-de Sitter space-times?, JHEP 03 (1999) 001 [hep-th/9902052] [INSPIRE].

V. Balasubramanian, P. Kraus and A.E. Lawrence, Bulk versus boundary dynamics in anti-de Sitter space-time, Phys. Rev. D 59 (1999) 046003 [hep-th/9805171] [INSPIRE].

G. Policastro and A. Starinets, On the absorption by near extremal black branes, Nucl. Phys. B 610 (2001) 117 [hep-th/0104065] [INSPIRE].

D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].

G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].

S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].

S. Grozdanov, K. Schalm and V. Scopelliti, Black hole scrambling from hydrodynamics, Phys. Rev. Lett. 120 (2018) 231601 [arXiv:1710.00921] [INSPIRE].

M. Blake, R.A. Davison, S. Grozdanov and H. Liu, Many-body chaos and energy dynamics in holography, JHEP 10 (2018) 035 [arXiv:1809.01169] [INSPIRE].

L.F. Alday, M. Kologlu and A. Zhiboedov, Holographic correlators at finite temperature, JHEP 06 (2021) 082 [arXiv:2009.10062] [INSPIRE].

M. Dodelson et al., Holographic thermal correlators from supersymmetric instantons, SciPost Phys. 14 (2023) 116 [arXiv:2206.07720] [INSPIRE].

N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [hep-th/9407087] [INSPIRE].

N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].

N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].

L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].

N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, in the proceedings of the 16th international congress on mathematical physics, (2009), p. 265 [https://doi.org/10.1142/9789814304634_0015] [arXiv:0908.4052] [INSPIRE].

G. Aminov, A. Grassi and Y. Hatsuda, Black hole quasinormal modes and Seiberg-Witten theory, Annales Henri Poincaré 23 (2022) 1951 [arXiv:2006.06111] [INSPIRE].

S. Musiri and G. Siopsis, Asymptotic form of quasinormal modes of large AdS black holes, Phys. Lett. B 576 (2003) 309 [hep-th/0308196] [INSPIRE].

J. Barragán Amado, B. Carneiro Da Cunha and E. Pallante, Scalar quasinormal modes of Kerr-AdS5, Phys. Rev. D 99 (2019) 105006 [arXiv:1812.08921] [INSPIRE].

J.B. Amado, B.C. da Cunha and E. Pallante, Quasinormal modes of scalar fields on small Reissner-Nordström-AdS5 black holes, Phys. Rev. D 105 (2022) 044028 [arXiv:2110.08349] [INSPIRE].

M. Piątek and A.R. Pietrykowski, Solving Heun’s equation using conformal blocks, Nucl. Phys. B 938 (2019) 543 [arXiv:1708.06135] [INSPIRE].

F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].

F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].

F.A. Dolan and H. Osborn, Conformal partial waves: further mathematical results, arXiv:1108.6194 [INSPIRE].

G. Bonelli, C. Iossa, D. Panea Lichtig and A. Tanzini, Irregular Liouville correlators and connection formulae for Heun functions, Commun. Math. Phys. 397 (2023) 635 [arXiv:2201.04491] [INSPIRE].

P.P. Fiziev, The Heun functions as a modern powerful tool for research in different scientific domains, arXiv:1512.04025.

A. Ronveaux and F.M. Arscott, Heun’s differential equations, Oxford University Press, Oxford, U.K. (1995).

O. Lisovyy and A. Naidiuk, Perturbative connection formulas for Heun equations, J. Phys. A 55 (2022) 434005 [arXiv:2208.01604] [INSPIRE].

L.F. Alday et al., Loop and surface operators in N = 2 gauge theory and Liouville modular geometry, JHEP 01 (2010) 113 [arXiv:0909.0945] [INSPIRE].

K. Maruyoshi and M. Taki, Deformed prepotential, quantum integrable system and Liouville field theory, Nucl. Phys. B 841 (2010) 388 [arXiv:1006.4505] [INSPIRE].

M. Hortacsu, Heun functions and some of their applications in physics, Adv. High Ener. Phys. 2018 (2018) 1 [arXiv:1101.0471] [INSPIRE].

K. Kwon, J. Barragán Amado and B. Gwak, Absorption cross section in gravity’s rainbow from confluent Heun equation, arXiv:2307.12824 [INSPIRE].

S. He and Y. Li, Holographic Euclidean thermal correlator, arXiv:2308.13518 [INSPIRE].

M. Dodelson, C. Iossa, R. Karlsson and A. Zhiboedov, A thermal product formula, arXiv:2304.12339 [INSPIRE].

S. Giusto, C. Iossa and R. Russo, The black hole behind the cut, JHEP 10 (2023) 050 [arXiv:2306.15305] [INSPIRE].

G. Aminov et al., Black hole perturbation theory and multiple polylogarithms, arXiv:2307.10141 [INSPIRE].

A. Bhatta and T. Mandal, Exact thermal correlators of holographic CFTs, JHEP 02 (2023) 222 [arXiv:2211.02449] [INSPIRE].

D. Birmingham, Topological black holes in anti-de Sitter space, Class. Quant. Grav. 16 (1999) 1197 [hep-th/9808032] [INSPIRE].

R. Emparan, AdS membranes wrapped on surfaces of arbitrary genus, Phys. Lett. B 432 (1998) 74 [hep-th/9804031] [INSPIRE].

R. Emparan, AdS/CFT duals of topological black holes and the entropy of zero energy states, JHEP 06 (1999) 036 [hep-th/9906040] [INSPIRE].

Y. Ahn, V. Jahnke, H.-S. Jeong and K.-Y. Kim, Scrambling in hyperbolic black holes: shock waves and pole-skipping, JHEP 10 (2019) 257 [arXiv:1907.08030] [INSPIRE].

R.-G. Cai and A. Wang, Thermodynamics and stability of hyperbolic charged black holes, Phys. Rev. D 70 (2004) 064013 [hep-th/0406057] [INSPIRE].

S.M. Hosseini, C. Toldo and I. Yaakov, Supersymmetric Rényi entropy and charged hyperbolic black holes, JHEP 07 (2020) 131 [arXiv:1912.04868] [INSPIRE].

A. Svesko, Extending charged holographic Rényi entropy, Class. Quant. Grav. 38 (2021) 135024 [arXiv:2011.08258] [INSPIRE].

X. He, B. Wang, R.-G. Cai and C.-Y. Lin, Signature of the black hole phase transition in quasinormal modes, Phys. Lett. B 688 (2010) 230 [arXiv:1002.2679] [INSPIRE].

Y.-M. Huang, Y. Tian, X.-N. Wu and H. Zhang, The topological RN-AdS black holes cannot be overcharged by the new version of gedanken experiment, Phys. Lett. B 829 (2022) 137031 [arXiv:2203.00988] [INSPIRE].

L.-Y. Hung, R.C. Myers, M. Smolkin and A. Yale, Holographic calculations of Rényi entropy, JHEP 12 (2011) 047 [arXiv:1110.1084] [INSPIRE].

H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].

R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].

J.R. David and S. Kumar, Thermal one point functions, large d and interior geometry of black holes, JHEP 03 (2023) 256 [arXiv:2212.07758] [INSPIRE].

M. Matone, Instantons and recursion relations in N = 2 SUSY gauge theory, Phys. Lett. B 357 (1995) 342 [hep-th/9506102] [INSPIRE].

M. Parikh and P. Samantray, Rindler-AdS/CFT, JHEP 10 (2018) 129 [arXiv:1211.7370] [INSPIRE].

B. Ahn et al., Holographic teleportation in higher dimensions, JHEP 07 (2021) 219 [arXiv:2011.13807] [INSPIRE].

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Journal of High Energy Physics

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