# Black holes from CFT: Universality of correlators at large c

## TL;DR

This paper demonstrates that in large central charge 2D CFTs with sparse spectra, thermal correlators of light operators are universally determined by the light spectrum, matching AdS$_3$ gravity predictions through modular invariance constraints.

## Contribution

It extends the universality of thermodynamics to correlation functions, showing they are computed by universal backgrounds (thermal AdS and BTZ) with corrections exponentially suppressed.

## Key findings

- Thermal correlators are determined by light spectrum data.
- Witten diagrams on universal backgrounds reproduce correlators order by order.
- Correlators exhibit exponential suppression of corrections 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.