On asymptotic symmetries of 3d extended supergravities

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.

Celestial Holography: Lectures on Asymptotic Symmetries

“…It is realized as asymptotic symmetry group of the simplest theory of 3d supergravity [119]. Larger supersymmetric extensions have been considered in [120][121][122][123][124][125][126][127][128][129][130].…”

Maximally $\cal{N}$-extended super-BMS$_3$ algebras and Generalized 3D Gravity Solutions

“…Note that the non-linear terms are a manifestation of the generic choice of representation for the internal symmetries. Earlier non-linear extension of the BMS 3 algebra were observed in [30], but in that case they originated by allowing fluctuation in the conformal factor of the boundary metric. In our construction, the boundary metric is always fixed to Minkowski.…”

Maximally $$ \mathcal{N} $$ -extended super-BMS3 algebras and generalized 3D gravity solutions

“…Earlier non-linear extension of the BMS 3 algebra were observed in [30], but in that case they originated by allowing fluctuation in the conformal factor of the boundary metric. In our construction, the boundary metric is always fixed to Minkowski.…”