Abstract
We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in d dimensions in terms of the c-anomaly coefficient. By including α′ corrections to the black brane background, we reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula. When the dimensions satisfy ∆i = ∆j + ∆k, the thermal 3-point function satisfies a factorization property. We argue that in d > 2 factorization is a reflection of the semiclassical regime.
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].
S. El-Showk and K. Papadodimas, Emergent Spacetime and Holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [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].
L.F. Alday, M. Kologlu and A. Zhiboedov, Holographic correlators at finite temperature, JHEP 06 (2021) 082 [arXiv:2009.10062] [INSPIRE].
N. Lashkari, A. Dymarsky and H. Liu, Eigenstate Thermalization Hypothesis in Conformal Field Theory, J. Stat. Mech. 1803 (2018) 033101 [arXiv:1610.00302] [INSPIRE].
A.L. Fitzpatrick and K.-W. Huang, Universal Lowest-Twist in CFTs from Holography, JHEP 08 (2019) 138 [arXiv:1903.05306] [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].
R. Karlsson, A. Parnachev and P. Tadić, Thermalization in Large-N CFTs, arXiv:2102.04953 [INSPIRE].
T. Klose and T. McLoughlin, A light-cone approach to three-point functions in AdS5 × S5, JHEP 04 (2012) 080 [arXiv:1106.0495] [INSPIRE].
E.I. Buchbinder and A.A. Tseytlin, Semiclassical correlators of three states with large S5 charges in string theory in AdS5 × S5, Phys. Rev. D 85 (2012) 026001 [arXiv:1110.5621] [INSPIRE].
J.A. Minahan, Holographic three-point functions for short operators, JHEP 07 (2012) 187 [arXiv:1206.3129] [INSPIRE].
A. Dymarsky and M. Smolkin, Krylov complexity in conformal field theory, Phys. Rev. D 104 (2021) L081702 [arXiv:2104.09514] [INSPIRE].
P. Kraus, H. Ooguri and S. Shenker, Inside the horizon with AdS/CFT, Phys. Rev. D 67 (2003) 124022 [hep-th/0212277] [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].
A. Hamilton, D.N. Kabat, G. Lifschytz and D.A. Lowe, Local bulk operators in AdS/CFT: A Holographic description of the black hole interior, Phys. Rev. D 75 (2007) 106001 [Erratum ibid. 75 (2007) 129902] [hep-th/0612053] [INSPIRE].
V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, Bulk and Transhorizon Measurements in AdS/CFT, JHEP 10 (2012) 165 [arXiv:1201.3664] [INSPIRE].
K. Papadodimas and S. Raju, An Infalling Observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].
T. Hartman and J. Maldacena, Time Evolution of Entanglement Entropy from Black Hole Interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
M. Dodelson and H. Ooguri, Singularities of thermal correlators at strong coupling, Phys. Rev. D 103 (2021) 066018 [arXiv:2010.09734] [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].
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].
H. Osborn and A.C. Petkou, Implications of conformal invariance in field theories for general dimensions, Annals Phys. 231 (1994) 311 [hep-th/9307010] [INSPIRE].
F. Bastianelli, S. Frolov and A.A. Tseytlin, Three point correlators of stress tensors in maximally supersymmetric conformal theories in D = 3 and D = 6, Nucl. Phys. B 578 (2000) 139 [hep-th/9911135] [INSPIRE].
S.M. Chester, J. Lee, S.S. Pufu and R. Yacoby, The \( \mathcal{N} \) = 8 superconformal bootstrap in three dimensions, JHEP 09 (2014) 143 [arXiv:1406.4814] [INSPIRE].
S. Dobashi, H. Shimada and T. Yoneya, Holographic reformulation of string theory on AdS5 × S5 background in the PP wave limit, Nucl. Phys. B 665 (2003) 94 [hep-th/0209251] [INSPIRE].
S. Dobashi and T. Yoneya, Resolving the holography in the plane-wave limit of AdS/CFT correspondence, Nucl. Phys. B 711 (2005) 3 [hep-th/0406225] [INSPIRE].
R.A. Janik, P. Surowka and A. Wereszczynski, On correlation functions of operators dual to classical spinning string states, JHEP 05 (2010) 030 [arXiv:1002.4613] [INSPIRE].
Y. Gobeil, A. Maloney, G.S. Ng and J.-q. Wu, Thermal Conformal Blocks, SciPost Phys. 7 (2019) 015 [arXiv:1802.10537] [INSPIRE].
P. Kovtun and A. Ritz, Black holes and universality classes of critical points, Phys. Rev. Lett. 100 (2008) 171606 [arXiv:0801.2785] [INSPIRE].
I.R. Klebanov and A.A. Tseytlin, Entropy of near extremal black p-branes, Nucl. Phys. B 475 (1996) 164 [hep-th/9604089] [INSPIRE].
M. Becker, Y. Cabrera and N. Su, Finite-temperature three-point function in 2D CFT, JHEP 09 (2014) 157 [arXiv:1407.3415] [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].
H. Liu and A.A. Tseytlin, Dilaton-fixed scalar correlators and AdS5 × S5 — SYM correspondence, JHEP 10 (1999) 003 [hep-th/9906151] [INSPIRE].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Extremal correlators in the AdS/CFT correspondence, hep-th/9908160 [INSPIRE].
L.A. Gaumé, D. Orlando and S. Reffert, Selected topics in the large quantum number expansion, Phys. Rept. 933 (2021) 2180 [arXiv:2008.03308] [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: 2105.13909
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
Rodriguez-Gomez, D., Russo, J.G. Thermal correlation functions in CFT and factorization. J. High Energ. Phys. 2021, 49 (2021). https://doi.org/10.1007/JHEP11(2021)049
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2021)049