Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity

TL;DR

This paper explores the asymptotic symmetries of three-dimensional extended AdS supergravity, revealing their structure as extended superconformal algebras and connecting them to super-Liouville theory, with implications for AdS/CFT correspondence.

Contribution

It systematically derives the superconformal symmetry algebras from Chern-Simons supergravity and generalizes spectral flow in this context.

Findings

Asymptotic symmetry algebra is the extended superconformal algebra with quadratic nonlinearities.

Super-Liouville action realization of the superconformal algebra.

Generalization of spectral flow for extended superconformal algebras.

Abstract

We investigate systematically the asymptotic dynamics and symmetries of all three-dimensional extended AdS supergravity models. First, starting from the Chern-Simons formulation, we show explicitly that the (super)anti-de Sitter boundary conditions imply that the asymptotic symmetry algebra is the extended superconformal algebra with quadratic nonlinearies in the currents. We then derive the super-Liouville action by solving the Chern-Simons theory and obtain a realization of the superconformal algebras in terms of super-Liouville fields. Finally, we discuss the possible periodic conditions that can be imposed on the generators of the algebra and generalize the spectral flow analysed previously in the context of the $N$-extended linear superconformal algebras with $N \leq 4$. The $(2+1)$-AdS/2-CFT correspondence sheds a new light on the properties of the nonlinear superconformal algebras. It also provides a general and natural interpretation of the spectral flow.