${\text{Super}\text{−}\mathrm{BMS}}_4$ algebras—also called ${\mathrm{BMS}}_4$ superalgebras—are graded extensions of the ${\mathrm{BMS}}_4$ 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) ${\text{super}\text{−}\mathrm{BMS}}_4$ algebra containing an infinite number of fermionic generators, which we denote ${\mathrm{SBMS}}_4$. These boundary conditions are not only invariant under ${\mathrm{SBMS}}_4$ 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 ${\mathrm{SBMS}}_4$ algebra. One finds, in particular, that the graded brackets between the fermionic generators yield all the ${\mathrm{BMS}}_4$ supertranslations, of which they provide therefore “square roots”.

• Received 26 August 2021
• Accepted 18 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.L121702

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Published by the American Physical Society