Supersymmetrization of deformed BMS algebras

TL;DR

This paper develops an $ ext{N}=2$ supersymmetric extension of deformed BMS algebras, revealing new central extensions and constraints on possible extensions with $U(1)$ symmetries in three and four dimensions.

Contribution

It constructs the most general $ ext{N}=2$ supersymmetric deformations of $W(a,b)$ and $W(a,b;ar{a},ar{b})$ algebras, including new central extensions and extension constraints.

Findings

Found a new central extension of $ ext{N}=2$ $ ext{BMS}_3$ algebra.

Showed that certain $U(1)$ extensions are not possible with linear and quadratic structure constants.

Identified constraints on $U(1)_V imes U(1)_A$ extensions of $ ext{BMS}_4$ algebra.

Abstract

$W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebras are deformations of ${\mathfrak{bms}_3}$ and ${\mathfrak{bms}_4}$ algebra respectively. We present an $\mathcal{N}=2$ supersymmetric extension of $W(a,b)$ and $W(a,b;\bar{a},\bar{b})$ algebra in presence of $R-$symmetry generators that rotate the two supercharges. For $W(a,b)$ our construction includes most generic central extensions of the algebra. In particular we find that $\mathcal{N}=2$ ${\mathfrak{bms}_3}$ algebra admits a new central extension that has so far not been reported in the literature. For $W(a,b;\bar{a},\bar{b})$, we find that an infinite $U(1)_V \times U(1)_A$ extension of the algebra is not possible with linear and quadratic structure constants for generic values of the deformation parameters. This implies a similar constraint for $U(1)_V \times U(1)_A$ extension of $\mathcal{N}=2$ ${\mathfrak{bms}_4}$ algebra.