Conformal bootstrap, universality and gravitational scattering

Abstract

We use the conformal bootstrap equations to study the non-perturbative\ngravitational scattering between infalling and outgoing particles in the\nvicinity of a black hole horizon in AdS. We focus on irrational 2D CFTs with\nlarge $c$ and only Virasoro symmetry. The scattering process is described by\nthe matrix element of two light operators (particles) between two heavy states\n(BTZ black holes). We find that the operator algebra in this regime is (i)\nuniversal and identical to that of Liouville CFT, and (ii) takes the form of an\nexchange algebra, specified by an R-matrix that exactly matches with the\nscattering amplitude of 2+1 gravity. The R-matrix is given by a quantum\n6j-symbol and the scattering phase by the volume of a hyperbolic tetrahedron.\nWe comment on the relevance of our results to scrambling and the holographic\nreconstruction of the bulk physics near black hole horizons.\n