Abstract
We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian mathcal{N} = 1 theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic S2 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 mathcal{N} = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.
Highlights
Momentum of the soft photon. (The generalization to theories with magnetically charged particles was described in [2].) The precise form of S is essentially determined by Lorentz and gauge invariance and will be reviewed below
The infinite-dimensional fermionic symmetry resides in the same N = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem
The universal soft behavior of gauge boson amplitudes was recently traced back to the existence of infinitely many symmetries that act on asymptotic scattering states at Minkowskian null infinity, i.e. asymptotic symmetries, whose Ward identities are equivalent to the soft theorems [2, 53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69]
Summary
We will use the conventions of [73]. As was stated in the introduction, we will consider U(1) gauge theories with N = 1 supersymmetry. The current multiplet J encodes all couplings of the gauge theory to charged matter, as well as possible self-interactions due to higher-derivative terms, such as those indicated in (2.4). It is helpful to keep in mind the simplest theory in this class, which consists of a single massless, minimally coupled chiral multiplet of charge q, with canonical kinetic terms and no superpotential or higher-derivative interactions.. It is helpful to keep in mind the simplest theory in this class, which consists of a single massless, minimally coupled chiral multiplet of charge q, with canonical kinetic terms and no superpotential or higher-derivative interactions.7 In this theory, the operators in the current multiplet J are given by KB = qΦΦ ,.
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