Extended Supersymmetric BMS$_3$ algebras and Their Free Field Realisations

TL;DR

This paper explores supersymmetric extensions of the three-dimensional BMS algebra, deriving new algebraic structures through contractions of superconformal algebras and constructing their free field realizations.

Contribution

It introduces the most general supersymmetric BMS$_3$ algebras with central extensions and provides free field realizations for these extended algebras.

Findings

Extended supersymmetric BMS$_3$ algebras derived from superconformal contractions

Identification that BMS/GCA correspondence does not generally hold for supersymmetric systems

Construction of free field realizations using $eta$-$ abla$ and ${rak b}$-${rak c}$ systems

Abstract

We study $N=(2,4,8)$ supersymmetric extensions of the three dimensional BMS algebra (BMS$_3$) with most generic possible central extensions. We find that $N$-extended supersymmetric BMS$_3$ algebras can be derived by a suitable contraction of two copies of the extended superconformal algebras. Extended algebras from all the consistent contractions are obtained by scaling left-moving and right-moving supersymmetry generators symmetrically, while Virasoro and R-symmetry generators are scaled asymmetrically. On the way, we find that the BMS/GCA correspondence does not in general hold for supersymmetric systems. Using the $\beta$-$\gamma$ and the ${\mathfrak b}$-${\mathfrak c}$ systems, we construct free field realisations of all the extended super-BMS$_3$ algebras.