Black holes from CFT: Universality of correlators at large c

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. This thermodynamics matches that of AdS${}_3$ 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.

arXiv comment18 pages. v2: minor edits

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• Bulk entanglement entropy in perturbative excited states
• Parity and the modular bootstrap
• Permutation Orbifolds and Chaos
• The Holographic Landscape of Symmetric Product Orbifolds
• The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds
• Semiclassical Gravity from Averaged Boundaries in two-dimensional BCFTs
• Light-state Dominance from the Conformal Bootstrap
• Semi-classical BMS-blocks from the Oscillator Construction
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• Aspects of the S transformation Bootstrap
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• Universality in the OPE Coefficients of Holographic 2d CFTs
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