Abstract
Two-dimensional conformal field theories at large central charge and with a sufficiently sparse spectrum of light states have been shown to exhibit universal thermodynamics [1]. This thermodynamics matches that of AdS3 gravity, with a Hawking-Page transition between thermal AdS and the BTZ black hole. We extend these results to correlation functions of light operators. Upon making some additional assumptions, such as large c factorization of correlators, we establish that the thermal AdS and BTZ solutions emerge as the universal backgrounds for the computation of correlators. In particular, Witten diagrams computed on these backgrounds yield the CFT correlators, order by order in a large c expansion, with exponentially small corrections. In pure CFT terms, our result is that thermal correlators of light operators are determined entirely by light spectrum data. Our analysis is based on the constraints of modular invariance applied to the torus two-point function.
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References
T. Hartman, C.A. Keller and B. Stoica, Universal spectrum of 2D conformal field theory in the large c limit, JHEP 09 (2014) 118 [arXiv:1405.5137] [INSPIRE].
D. Harlow, Jerusalem lectures on black holes and quantum information, Rev. Mod. Phys. 88 (2016) 15002 [arXiv:1409.1231] [INSPIRE].
S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black holes: complementarity or firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
S. Hellerman, A universal inequality for CFT and quantum gravity, JHEP 08 (2011) 130 [arXiv:0902.2790] [INSPIRE].
A. Belin, C.A. Keller and I.G. Zadeh, Genus two partition functions and Rényi entropies of large c CFTs, arXiv:1704.08250 [INSPIRE].
J. Cardy, A. Maloney and H. Maxfield, A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance, arXiv:1705.05855 [INSPIRE].
A. Maloney, H. Maxfield and G.S. Ng, A conformal block Farey tail, JHEP 06 (2017) 117 [arXiv:1609.02165] [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].
C.-M. Chang and Y.-H. Lin, Bootstrapping 2D CFTs in the semiclassical limit, JHEP 08 (2016) 056 [arXiv:1510.02464] [INSPIRE].
C.-M. Chang and Y.-H. Lin, Bootstrap, universality and horizons, JHEP 10 (2016) 068 [arXiv:1604.01774] [INSPIRE].
S. Collier, Y.-H. Lin and X. Yin, Modular bootstrap revisited, arXiv:1608.06241 [INSPIRE].
S. Collier, P. Kravchuk, Y.-H. Lin and X. Yin, Bootstrapping the spectral function: on the uniqueness of Liouville and the universality of BTZ, arXiv:1702.00423 [INSPIRE].
S. El-Showk and K. Papadodimas, Emergent spacetime and holographic CFTs, JHEP 10 (2012) 106 [arXiv:1101.4163] [INSPIRE].
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from conformal field theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
A. Belin, B. Freivogel, R.A. Jefferson and L. Kabir, Sub-AdS scale locality in AdS 3 /CFT 2, JHEP 04 (2017) 147 [arXiv:1611.08601] [INSPIRE].
D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, OPE convergence in conformal field theory, Phys. Rev. D 86 (2012) 105043 [arXiv:1208.6449] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
A. Belin, Permutation orbifolds and chaos, arXiv:1705.08451 [INSPIRE].
V. Balasubramanian, P. Kraus and M. Shigemori, Massless black holes and black rings as effective geometries of the D1-D5 system, Class. Quant. Grav. 22 (2005) 4803 [hep-th/0508110] [INSPIRE].
E. Shaghoulian, Modular forms and a generalized Cardy formula in higher dimensions, Phys. Rev. D 93 (2016) 126005 [arXiv:1508.02728] [INSPIRE].
E. Shaghoulian, Black hole microstates in AdS, Phys. Rev. D 94 (2016) 104044 [arXiv:1512.06855] [INSPIRE].
A. Belin, J. de Boer, J. Kruthoff, B. Michel, E. Shaghoulian and M. Shyani, Universality of sparse d > 2 conformal field theory at large-N, JHEP 03 (2017) 067 [arXiv:1610.06186] [INSPIRE].
E. Shaghoulian, Modular invariance on S 1 × S 3 and circle fibrations, arXiv:1612.05257 [INSPIRE].
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ArXiv ePrint: 1706.00771
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Kraus, P., Sivaramakrishnan, A. & Snively, R. Black holes from CFT: universality of correlators at large c . J. High Energ. Phys. 2017, 84 (2017). https://doi.org/10.1007/JHEP08(2017)084
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DOI: https://doi.org/10.1007/JHEP08(2017)084