On Asymptotic Symmetries of 3d Extended Supergravities

TL;DR

This paper explores the asymptotic symmetry algebras in three-dimensional extended supergravities, extending boundary conditions from $AdS_3$ to supergravity and analyzing their algebraic structures, including superalgebras and $BMS_3$ extensions.

Contribution

It generalizes boundary conditions and computes asymptotic symmetries for 3d supergravities, revealing new superalgebra structures and extensions of $BMS_3$ without cosmological constant.

Findings

Boundary conditions extend to supergravity with compatible superalgebras.

Asymptotic symmetry algebras include superalgebra extensions of $BMS_3$.

Results connect holographic descriptions with supergravity boundary conditions.

Abstract

We study asymptotic symmetry algebras for classes of three dimensional supergravities with and without cosmological constant. In the first part we generalise some of the non-Dirichlet boundary conditions of $AdS_3$ gravity to extended supergravity theories, and compute their asymptotic symmetries. In particular, we show that the boundary conditions proposed to holographically describe the chiral induced gravity and Liouville gravity do admit extension to the supergravity contexts with appropriate superalgebras as their asymptotic symmetry algebras. In the second part we consider generalisation of the 3d $BMS$ computation to extended supergravities without cosmological constant, and show that their asymptotic symmetry algebras provide examples of nonlinear extended superalgebras containing the $BMS_3$ algebra.