An sl(2, R) current algebra from AdS_3 gravity

TL;DR

This paper establishes chiral boundary conditions in 3D gravity leading to an sl(2,R) current algebra symmetry, aligning with Polyakov's 2D induced gravity, and provides explicit solutions and charges.

Contribution

It introduces the most general boundary conditions compatible with recent boundary term formulations, resulting in an explicit sl(2,R) current algebra symmetry in AdS_3 gravity.

Findings

Asymptotic symmetry algebra is an sl(2,R) current algebra with level c/6.

Provides a fully non-linear Fefferman--Graham solution with charges.

Boundary conditions match those of Polyakov's 2D induced gravity.

Abstract

We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered by Polyakov. These are the most general boundary conditions consistent with the boundary terms introduced by Compere, Song and Strominger recently. We show that the asymptotic symmetry algebra of our boundary conditions is an sl(2,R) current algebra with level given by c/6. The fully non-linear solution in Fefferman--Graham coordinates is also provided along with its charges.