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

TL;DR

This work analyzes two distinct flat-space limits of 3D ${\cal N}=(1,1)$ AdS supergravity, uncovering a democratic (super-Poincaré) and a novel despotic (twisted) ${\cal N}=2$ theory. By prescribing suitable boundary conditions, the authors derive two ${\cal N}=2$ super-BMS$_3$ algebras, corresponding respectively to homogeneous and inhomogeneous super-GCA structures, thereby linking flat-space holography to tensionless-string limits. They derive energy bounds from the algebras, and compute both asymptotic and exact Killing spinors for bosonic zero modes in each theory, highlighting that supersymmetric solutions in the despotic case require vanishing angular momentum ${\cal J}$. The results illuminate how different flat-space contractions of ${\cal N}=(1,1)$ AdS$_3$ yield distinct asymptotic symmetries and supersymmetry realizations, with implications for flat-space holography and the structure of supersymmetric ground states.

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.