Asymptotic symmetries and dynamics of three-dimensional flat supergravity

TL;DR

This paper establishes a consistent set of asymptotic conditions for three-dimensional flat supergravity, revealing a supersymmetric extension of the BMS3 algebra with bounded energy and connections to AdS3 supergravity.

Contribution

It introduces a new set of asymptotic conditions for 3D flat supergravity and demonstrates the supersymmetric extension of the BMS3 algebra with central charges.

Findings

Supersymmetric extension of BMS3 algebra with central charge

Energy bounded from below with Minkowski or null orbifold ground states

Connection between flat supergravity and AdS3 supergravity via flat limit

Abstract

A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a supersymmetric extension of the BMS$_3$ algebra with an appropriate central charge. The energy is manifestly bounded from below with the ground state given by the null orbifold or Minkowski spacetime for periodic, respectively antiperiodic boundary conditions on the gravitino. These results are related to the corresponding ones in AdS$_3$ supergravity by a suitable flat limit. The analysis is generalized to the case of minimal flat supergravity with additional parity odd terms for which the Poisson algebra of canonical generators form a representation of the super-BMS$_3$ algebra with an additional central charge.