An sl(2, R) current algebra from AdS_3 gravity
Steven G. Avery, Rohan R. Poojary, Nemani V. Suryanarayana
TL;DR
The paper introduces chiral boundary conditions for $AdS_3$ gravity that reproduce the $sl(2,\mathbb{R})$ current algebra found in Polyakov's 2D induced gravity in light-cone gauge, showing these are the most general conditions compatible with CSS-type boundary terms. It constructs a full non-linear Fefferman–Graham bulk solution under these conditions and computes the associated BBC charges, obtaining a Virasoro-like Witt algebra together with an $sl(2,\mathbb{R})$ current algebra at level $k=c/6$ (with central charge $c=3l/(2G)$). The results bridge 3D gravity and 2D induced gravity via holography, and suggest avenues for including matter, exploring warped AdS$_3$ settings, and connecting to Liouville-type boundary dynamics. This work clarifies how different gauge fixings of the induced gravity boundary theory correspond to distinct bulk boundary conditions and holographic duals.
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.