Fermionic asymptotic symmetries in massless QED

TL;DR

This paper explores fermionic asymptotic symmetries in massless QED, revealing potential supersymmetric structures at the asymptotic level through soft electron emissions and their associated Ward identities.

Contribution

It introduces the first example of an asymptotic fermionic symmetry in a non-supersymmetric theory, linking soft electron emissions to asymptotic charge conservation.

Findings

Soft electron emission amplitude factorizes similarly to soft photon case.

Soft electron Ward identity suggests a fermionic asymptotic symmetry.

Potential supersymmetric algebra involving subleading soft photons.

Abstract

We consider soft electrons in massless QED at tree-level. The emission amplitude at leading order in the soft electron energy factorizes in a way similar to the soft photon case. We recast the soft electron factorization formula as a Ward identity of an asymptotic charge. This leads to the first example of an asymptotic fermionic symmetry in a theory with no conventional supersymmetry, suggesting that tree-level massless QED may posses an asymptotic supersymmetry algebra. Although our approach does not yet allow us to completely characterize the algebra, it suggests that subleading soft photons should feature in the anticommutator of two fermionic symmetry generators.