Super-BMS$_3$ algebras from $\mathcal{N}=2$ flat supergravities

TL;DR

This paper explores two flat space limits of three-dimensional $ ext{AdS}_3$ supergravity, deriving supersymmetric extensions of BMS algebras and analyzing their boundary conditions, energy bounds, and Killing spinors.

Contribution

It introduces a novel 'twisted' supergravity theory from a new flat limit and establishes supersymmetric BMS algebras with detailed boundary conditions and solution analysis.

Findings

Derived supersymmetric BMS algebras from flat limits

Proposed boundary conditions for asymptotic symmetries

Analyzed supersymmetric energy bounds and Killing spinors

Abstract

We consider two possible flat space limits of three dimensional $\mathcal{N} = (1,1)$ AdS supergravity. They differ by how the supercharges are scaled with the AdS radius $\ell$: the first limit (democratic) leads to the usual super-Poincare theory, while a novel `twisted' theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non- and ultra-relativistic limits of the $\mathcal{N}=(1,1)$ Virasoro algebra in two dimensions. Finally, we study the supersymmetric energy bounds and find the explicit form of the asymptotic and global Killing spinors of supersymmetric solutions in both flat space supergravity theories.