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Super-BMS$_4$ algebras -- also called BMS$_4$ superalgebras -- are gradedextensions of the BMS$_4$ algebra. They can be of two different types: they cancontain either a finite number or an infinite number of fermionic generators.We show in this letter that, with suitable boundary conditions on the gravitonand gravitino fields at spatial infinity, supergravity on asymptotically flatspaces 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 invariantunder SBMS$_4$, but also lead to a fully consistent canonical description ofthe supersymmetries, which have in particular well-defined Hamiltoniangenerators that close according to the nonlinear SBMS$_4$ algebra. One finds inparticular that the graded brackets between the fermionic generators yield allthe BMS$_4$ supertranslations, of which they provide therefore "square roots".

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