Abstract
We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator Ok and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of TnOk (being Tn the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. Iliesiu, M. Koloğlu, R. Mahajan, E. Perlmutter and D. Simmons-Duffin, The Conformal Bootstrap at Finite Temperature, JHEP 10 (2018) 070 [arXiv:1802.10266] [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].
D. Rodriguez-Gomez and J.G. Russo, Thermal correlation functions in CFT and factorization, JHEP 11 (2021) 049 [arXiv:2105.13909] [INSPIRE].
R. Karlsson, A. Parnachev and P. Tadić, Thermalization in Large-N CFTs, arXiv:2102.04953 [INSPIRE].
A.L. Fitzpatrick, K.-W. Huang and D. Li, Probing universalities in d > 2 CFTs: from black holes to shockwaves, JHEP 11 (2019) 139 [arXiv:1907.10810] [INSPIRE].
A.L. Fitzpatrick and K.-W. Huang, Universal Lowest-Twist in CFTs from Holography, JHEP 08 (2019) 138 [arXiv:1903.05306] [INSPIRE].
L.F. Alday, M. Koloğlu and A. Zhiboedov, Holographic correlators at finite temperature, JHEP 06 (2021) 082 [arXiv:2009.10062] [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, The Black hole singularity in AdS/CFT, JHEP 02 (2004) 014 [hep-th/0306170] [INSPIRE].
G. Festuccia and H. Liu, Excursions beyond the horizon: Black hole singularities in Yang-Mills theories. I, JHEP 04 (2006) 044 [hep-th/0506202] [INSPIRE].
V.E. Hubeny, H. Liu and M. Rangamani, Bulk-cone singularities & signatures of horizon formation in AdS/CFT, JHEP 01 (2007) 009 [hep-th/0610041] [INSPIRE].
V.E. Hubeny, Extremal surfaces as bulk probes in AdS/CFT, JHEP 07 (2012) 093 [arXiv:1203.1044] [INSPIRE].
M. Grinberg and J. Maldacena, Proper time to the black hole singularity from thermal one-point functions, JHEP 03 (2021) 131 [arXiv:2011.01004] [INSPIRE].
I. Amado and C. Hoyos-Badajoz, AdS black holes as reflecting cavities, JHEP 09 (2008) 118 [arXiv:0807.2337] [INSPIRE].
J. Engelsöy and B. Sundborg, Tidal excitation as mixing in thermal CFT, arXiv:2106.06520 [INSPIRE].
J. Erdmenger, C. Hoyos and S. Lin, Time Singularities of Correlators from Dirichlet Conditions in AdS/CFT, JHEP 03 (2012) 085 [arXiv:1112.1963] [INSPIRE].
M. Dodelson and H. Ooguri, Singularities of thermal correlators at strong coupling, Phys. Rev. D 103 (2021) 066018 [arXiv:2010.09734] [INSPIRE].
J.L. Cardy, Conformal invariance and universality in finite-size scaling, J. Phys. A 17 (1984) L385 [INSPIRE].
P. Kraus and A. Maloney, A cardy formula for three-point coefficients or how the black hole got its spots, JHEP 05 (2017) 160 [arXiv:1608.03284] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 534 (1998) 202 [hep-th/9805156] [INSPIRE].
J. Pawełczyk and S. Theisen, AdS5 × S5 black hole metric at \( \mathcal{O} \)(α′3), JHEP 09 (1998) 010 [hep-th/9808126] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2108.00277
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Krishna, H., Rodriguez-Gomez, D. Holographic thermal correlators revisited. J. High Energ. Phys. 2021, 139 (2021). https://doi.org/10.1007/JHEP11(2021)139
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2021)139