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

TL;DR

This work establishes that extended AdS$_3$ supergravity, formulated as a Chern-Simons theory, naturally yields nonlinear extended superconformal algebras as their asymptotic symmetries, with a classical Virasoro central charge $c=6k$. The boundary dynamics are shown to be governed by a (extended) super-Liouville theory obtained via Hamiltonian reduction of a gauged super-WZW model, providing explicit realizations of the superconformal generators in terms of Liouville fields. It also clarifies the spectrum of allowed boundary moddings (including spectral flow) and their physical interpretation within the AdS/CFT framework. The results offer a concrete bulk/boundary dictionary for nonlinear superconformal algebras and open avenues for extensions to related gravity/superconformal systems and higher-dimensional analogs.

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.