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arXiv · 2201.09853

Supersymmetrization of deformed BMS algebras

Nabamita Banerjee·Arpita Mitra·Debangshu Mukherjee·H. R. Safari
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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.

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Nabamita Banerjee, Arpita Mitra, Debangshu Mukherjee, H. R. Safari. 2022-01-24. Supersymmetrization of deformed BMS algebras. https://doi.org/10.1140/epjc/s10052-022-11036-y

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