Conserved currents for unconventional supersymmetric couplings of self-dual gauge fields

TL;DR

This paper explores supersymmetric couplings of self-dual gauge fields to higher-spin fields, revealing conserved currents and supermultiplets that extend the super-Poincaré algebra without classical limitations.

Contribution

It introduces a framework for supersymmetric self-dual gauge theories with arbitrarily extended super-Poincaré algebras and explicitly constructs equations of motion up to N=6.

Findings

Conserved currents are governed by supersymmetry.

The stress tensor is part of a conserved multiplet for N≥4.

Classical consistency allows unlimited extension N.

Abstract

Self-dual gauge potentials admit supersymmetric couplings to higher-spin fields satisfying interacting forms of the first order Dirac--Fierz equation. The interactions are governed by conserved currents determined by supersymmetry. These super-self-dual Yang-Mills systems provide on-shell supermultiplets of arbitrarily extended super-Poincar\'e algebras; classical consistency not setting any limit on the extension N. We explicitly display equations of motion up to the $N=6$ extension. The stress tensor, which vanishes for the $N\le 3$ self-duality equations, not only gets resurrected when $N=4$, but is then a member of a conserved multiplet of gauge-invariant tensors.