Super Virasoro Algebra From Supergravity

TL;DR

This paper explores the AdS3/CFT2 correspondence in three-dimensional supergravity, demonstrating the emergence of Virasoro and super Virasoro algebras at the boundary, with a focus on covariant construction and asymptotic symmetries.

Contribution

It constructs covariant currents for general coordinate invariance and local supersymmetry, and shows the boundary symmetry algebra includes Virasoro and super Virasoro structures.

Findings

Existence of Virasoro algebra at the boundary of AdS3.

Extension of one Virasoro algebra to super Virasoro algebra.

Well-defined Hamiltonian and supercharge in terms of geometric variables.

Abstract

We investigate AdS3/CFT2 correspondence in three dimensional supergravity. We construct a current for general coordinate invariance and that for local supersymmetry via covariant approach. Hamiltonian and supercharge are well defined in terms of vielbein and spin connection. After discussing asymptotic supersymmetry group at the boundary of AdS3 geometry, we show that there exist a direct product of Virasoro algebras at the boundary. We also show that one of them is extended to super Virasoro algebra.