Conformal Bootstrap, Universality and Gravitational Scattering

TL;DR

This paper employs the conformal bootstrap approach to analyze non-perturbative gravitational scattering near black hole horizons in AdS, revealing universal algebraic structures linked to Liouville CFT and 2+1 gravity.

Contribution

It demonstrates that the operator algebra in this regime is universal, matching Liouville CFT, and provides an exact R-matrix description of scattering matching 2+1 gravity amplitudes.

Findings

Operator algebra is universal and identical to Liouville CFT.

Scattering described by an R-matrix given by a quantum 6j-symbol.

Scattering phase related to hyperbolic tetrahedron volume.

Abstract

We use the conformal bootstrap equations to study the non-perturbative gravitational scattering between infalling and outgoing particles in the vicinity of a black hole horizon in AdS. We focus on irrational 2D CFTs with large $c$ and only Virasoro symmetry. The scattering process is described by the matrix element of two light operators (particles) between two heavy states (BTZ black holes). We find that the operator algebra in this regime is (i) universal and identical to that of Liouville CFT, and (ii) takes the form of an exchange algebra, specified by an R-matrix that exactly matches with the scattering amplitude of 2+1 gravity. The R-matrix is given by a quantum 6j-symbol and the scattering phase by the volume of a hyperbolic tetrahedron. We comment on the relevance of our results to scrambling and the holographic reconstruction of the bulk physics near black hole horizons.