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

Abstract

Super-BMS4 algebras - also called BMS4 superalgebras - are graded extensions of the BMS4 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-BMS4 algebra containing an infinite number of fermionic generators, which we denote SBMS4. These boundary conditions are not only invariant under SBMS4 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 SBMS4 algebra. One finds, in particular, that the graded brackets between the fermionic generators yield all the BMS4 supertranslations, of which they provide therefore "square roots".