Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations

Abstract

Super-BMS${}_4$ algebras -- also called BMS${}_4$ superalgebras -- are graded extensions of the BMS${}_4$ algebra. They can be of two different types: they can contain either a finite number or an infinite number of fermionic generators. We show in this letter that, with suitable boundary conditions on the graviton and gravitino fields at spatial infinity, supergravity on asymptotically flat spaces possesses as superalgebra of asymptotic symmetries a (nonlinear) super-BMS${}_4$ algebra containing an infinite number of fermionic generators, which we denote SBMS${}_4$. These boundary conditions are not only invariant under SBMS${}_4$, but also lead to a fully consistent canonical description of the supersymmetries, which have in particular well-defined Hamiltonian generators that close according to the nonlinear SBMS${}_4$ algebra. One finds in particular that the graded brackets between the fermionic generators yield all the BMS${}_4$ supertranslations, of which they provide therefore "square roots".

7 pages, no figures

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• Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis
• Supersymmetrization of deformed BMS algebras
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• Asymptotic $\mathcal{O}(r)$ gauge symmetries and gauge-invariant Poincaré generators in higher spacetime dimensions
• A novel supersymmetric extension of BMS symmetries at null infinity
• Conserved asymptotic charges for any massless particle
• BRST BMS4 Symmetry and its Cocycles from Horizontality Conditions
• On the nature of Bondi-Metzner-Sachs transformations
• On the geometric approach to the boundary problem in supergravity