Black holes from CFT: Universality of correlators at large c

TL;DR

The paper addresses when large-$c$ 2D CFTs with a sparse light spectrum yield universal correlation functions corresponding to black-hole backgrounds. By combining modular invariance of the torus two-point function with a set of reasonable large-$c$ assumptions, it shows that thermal correlators of light operators are determined entirely by light-spectrum data and can be computed from Witten diagrams on universal backgrounds: thermal AdS for $eta>2\pi$ and Euclidean BTZ for $eta<2\pi$, with corrections suppressed exponentially in $c$ or the light-cutoff $oldsymbol{}$. The analysis decomposes the two-point function into light, medium, and heavy sectors, bounding medium and off-diagonal contributions, and employs modular covariance to bound heavy-heavy terms, thereby proving LL-dominance order by order in $1/ ootrom{}{ oot}$. This extends the Hartman–Keller–Stoica program to correlators, providing a CFT-only derivation of bulk black-hole physics in AdS$_3$/CFT$_2$ and reinforcing the Hawking–Page transition as a universal feature in holographic theories.

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.