Supersymmetrization of deformed BMS algebras

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.

42 pages, no figure, Introduction and Conclusion expanded, two new appendices, new references added

References in corpus (16)

• Entropy of three-dimensional asymptotically flat cosmological solutions
• CHL Dyons and Statistical Entropy Function from D1-D5 System
• Asymptotic symmetries and dynamics of three-dimensional flat supergravity
• Null boundary phase space: slicings, news and memory
• Product Representation of Dyon Partition Function in CHL Models
• Dyon Spectrum in N=4 Supersymmetric Type II String Theories
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Super-BMS${}_3$ algebras from $\mathcal{N}=2$ flat supergravities
• Conservation and Integrability in Lower-Dimensional Gravity
• Asymptotic Expansion of the N=4 Dyon Degeneracy
• Asymptotic structure of $\mathcal{N}=2$ supergravity in 3D: extended super-BMS${}_3$ and nonlinear energy bounds
• Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations
• N=4 Supersymmetric BMS3 algebras from asymptotic symmetry analysis
• BMS4 Algebra, Its Stability and Deformations
• Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity
• Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity

Cited by in corpus (1)

• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism