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

TL;DR

This paper explores the asymptotic structure and symmetries of three-dimensional anti-de Sitter supergravity, establishing the superconformal algebra and computing the classical central charge, linking boundary conditions to boundary degrees of freedom.

Contribution

It provides precise asymptotic conditions for Rarita-Schwinger fields and demonstrates how these lead to superconformal symmetry and boundary degrees of freedom in 3D supergravity.

Findings

Superconformal algebra as asymptotic symmetry

Classical central charge matches pure gravity

Boundary conditions relate supercurrent to supercharges

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.