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

TL;DR

This paper demonstrates that supergravity on asymptotically flat spaces admits a nonlinear super-BMS$_4$ algebra with infinitely many fermionic generators, providing a supersymmetric extension of BMS$_4$ with well-defined Hamiltonian generators.

Contribution

It shows that suitable boundary conditions lead to a consistent superalgebra of asymptotic symmetries in supergravity, extending BMS$_4$ with infinite fermionic generators.

Findings

Supergravity admits a nonlinear super-BMS$_4$ algebra with infinite fermionic generators.

Boundary conditions ensure invariance and a consistent canonical structure.

Fermionic generators' brackets produce all BMS$_4$ 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".