Anti-de Sitter/CFT Correspondence in Three-Dimensional Supergravity

TL;DR

This paper analyzes AdS$_3$ supergravity by imposing precise boundary conditions on the Rarita–Schwinger fields within the Chern-Simons framework with the group $OSp(1|2)\times OSp(1|2)$. It shows the asymptotic symmetry is the (1,1) super-Virasoro algebra with central charge $c=\dfrac{3l}{2G}$ (equivalently $c=6k$ with $k=\dfrac{l}{4G}$), and that a twofold boundary dynamics reduce to 2D induced supergravity, with the WZW currents transmuted into supercharges. The boundary theory is further related to 2D super-Liouville through Hamiltonian reduction, revealing how supersymmetry emerges on the boundary from 3D AdS asymptotics. These results reinforce the AdS/CFT picture in 3D, providing a concrete link between bulk supergravity and boundary superconformal dynamics and offering a route to microstate counting for AdS$_3$ black holes.

Abstract

Anti-de Sitter supergravity models are considered in three dimensions. Precise asymptotic conditions involving a chiral projection are given on the Rarita-Schwinger fields. Together with the known boundary conditions on the bosonic fields, these ensure that the asymptotic symmetry algebra is the superconformal algebra. The classical central charge is computed and found to be equal to the one of pure gravity. It is also indicated that the asymptotic degrees of freedom are described by 2D "induced supergravity" and that the boundary conditions "transmute" the non-vanishing components of the WZW supercurrent into the supercharges.