Infinite-Dimensional Fermionic Symmetry in Supersymmetric Gauge Theories

TL;DR

The paper identifies an infinite-dimensional fermionic asymptotic symmetry in four-dimensional $\mathcal N=1$ abelian gauge theories with charged matter, parameterized by a spinor-valued function on $S^2$ at null infinity. The corresponding fermionic charges ${\mathscr F}[\chi]$ form a supermultiplet with the bosonic large-gauge charges ${\mathscr E}[\varepsilon]$, and their Ward identities reproduce the soft photino theorem, mirroring the bosonic soft-photon structure. By developing the full asymptotic framework—kinematics, photon and photino falloffs, and current multiplets—the authors derive explicit hard and soft components of ${\mathscr F}[\chi]$, show its conservation, and compute its action on matter fields, connecting infrared symmetries to SUSY representations. This extends the infrared symmetry story to the fermionic sector and highlights a SUSY-linked cloud of asymptotic symmetries with potential implications for IR dynamics and memory phenomena in supersymmetric gauge theories.

Abstract

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.