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

TL;DR

This paper derives the maximal extended super-BMS3 algebra for 3D supergravity, revealing its structure, supersymmetric bounds, and specific solutions, including non-supersymmetric cosmological states and their entropy.

Contribution

It constructs the maximal extended super-BMS3 algebra with non-linear supercharge anticommutators and analyzes its physical implications in 3D supergravity.

Findings

Derived the super-BMS3 algebra with non-linear fermionic relations.

Identified the supersymmetric energy bounds and Killing spinors.

Found and characterized the ground state solutions and their entropy.

Abstract

We consider the maximal $\cal{N}-$extended supergravity theory in 3 dimensions with fermionic generators transforming under real but non necessarily irreducible representations of the internal algebra. We obtain the symmetry algebra at null infinity preserving boundary conditions of asymptotically flat solutions, i.e. the maximal $\cal{N}-$extended super-BMS$_3$ algebra, which possesses non-linear correction in the anti-commutators of supercharges. We present the supersymmetric energy bound and derive the explicit form of the asymptotic Killing spinors. We also find the most generic circular symmetric ground state of the theory, which corresponds to a non-supersymmetric cosmological solutions and derive their entropy.