Asymptotic symmetries and dynamics of three-dimensional flat supergravity

TL;DR

The paper constructs consistent asymptotic conditions for 3D flat $\mathcal{N}=1$ supergravity, showing the asymptotic symmetry algebra is the supersymmetric extension of BMS$_3$ (super-BMS$_3$) with a central charge $c_2=3/G$ and a vanishing $c_1$. It derives the reduced phase space, canonical charges, and energy bounds via both classical and quantum approaches, and analyzes Killing spinors for bosonic backgrounds. It further connects these flat-space results to asymptotically AdS$_3$ supergravity through a careful flat-limit procedure, confirming the contraction to super-BMS$_3$, and explores a generalized “reloaded” flat supergravity theory where a parity-odd Lorentz term introduces an additional central charge $c_1=3\mu/G$. Overall, the work clarifies how supersymmetry constrains 3D flat gravity and its relation to AdS holography, including extensions with extra central extensions.

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.