Anti-de Sitter holography for gravity and higher spin theories in two dimensions

TL;DR

This work establishes AdS$_2$ holography for 2d dilaton gravity and extends it to 2d higher-spin theories using a Poisson-Sigma-model framework. It shows the asymptotic symmetry is a single copy of the Virasoro algebra with positive central charge $c$, though canonical boundary charges are finite but non-integrable, complicating a direct canonical realization; in spin-3 gravity the asymptotic symmetry becomes the $W_3$ algebra with positive central charge. The results provide the first explicit holographic descriptions of 2d higher-spin gravity and illuminate subtleties of boundary charges in two dimensions, offering a concrete setting to study chiral CFT duals and potential extensions to broader AdS$_2$/CFT$_1$ correspondences.

Abstract

We provide a holographic description of two-dimensional dilaton gravity with Anti-de Sitter boundary conditions. We find that the asymptotic symmetry algebra consists of a single copy of the Virasoro algebra with non-vanishing central charge and point out difficulties with the standard canonical treatment. We generalize our results to higher spin theories and thus provide the first examples of two-dimensional higher spin gravity with holographic description. For spin-3 gravity we find that the asymptotic symmetry algebra is a single copy of the W_3-algebra.