Infinite-Dimensional Fermionic Symmetry in Supersymmetric Gauge Theories

We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian ${\cal N}=1$ theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic $S^2$ at null infinity. It is not manifest at the level of the Lagrangian, but acts non-trivially on physical states, and its Ward identity is the soft photino theorem. The infinite-dimensional fermionic symmetry resides in the same ${\cal N}=1$ supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.