Manifestly invariant actions for harmonic self-dual gauge theory

TL;DR

This paper explores new harmonic space formulations of self-dual Yang-Mills fields, introducing covariant harmonic actions and analyzing their properties, which could deepen understanding of self-dual gauge theories.

Contribution

It presents alternative harmonic space descriptions and constructs invariant actions for four-dimensional self-dual Yang-Mills fields, including covariant harmonic formulations.

Findings

Harmonic space provides a framework for self-dual gauge fields.

Invariant harmonic actions are constructed for self-dual equations.

Covariant harmonic fields relate to higher-spin fields.

Abstract

We discuss alternative descriptions of four-dimensional self-dual Yang-Mills fields in harmonic space with additional commuting spinor coordinates. In particular, the linear analyticity equation and nonlinear covariant harmonic-field equations are studied. A covariant harmonic field can be treated as an infinite set of ordinary four-dimensional fields with higher spins. We analyze different constructions of invariant harmonic-field actions corresponding to the self-dual harmonic equations.