Supersymmetrization of deformed BMS algebras

Abstract

Abstract The W(a, b) and $$W(a,b;\bar{a},\bar{b})$$ W ( a , b ; a ¯ , b ¯ ) algebras are deformations of $$\mathfrak {bms}_{3}$$ bms 3 and $$\mathfrak {bms}_{4}$$ bms 4 algebras, respectively. We present a $$\mathcal {N}=2$$ N = 2 supersymmetric extension of both algebras in the presence of Rsymmetry generators that rotates the two supercharges. Our construction provides the most generic central extensions of the W(a, b) algebra. In particular, we find that $$\mathcal {N}=2$$ N = 2 $$\mathfrak {bms}_{3}$$ bms 3 algebra admits a new central extension. On the other hand, we explicitly demonstrate that an infinite $$U(1)_V \times U(1)_A$$ U ( 1 ) V × U ( 1 ) A extension of the $$W(a,b;\bar{a},\bar{b})$$ W ( a , b ; a ¯ , b ¯ ) algebra corresponding to the $$R-$$ R - symmetry is not possible for linear and quadratic structure constants with generic deformation parameters. This also implies that the infinite R symmetry considered in our analysis is broken for the $$\mathcal {N}=2 \, \mathfrak {bms}_{4}$$ N = 2 bms 4 algebra.