An action for N=4 supersymmetric self-dual Yang-Mills theory

TL;DR

This paper formulates an $N=4$ supersymmetric self-dual Yang-Mills theory in four-dimensional space with signature $(2,2)$ using harmonic superspace, providing a manifestly invariant action and reformulating constraints as curvature conditions.

Contribution

It introduces a new harmonic superspace formulation and a Chern-Simons type action for the $N=4$ supersymmetric self-dual Yang-Mills theory, extending previous light-cone approaches.

Findings

Reformulation of on-shell constraints as curvature conditions.

Construction of a manifestly $SO(2,2)$ invariant superspace action.

Equivalence to the light-cone superfield action of Siegel.

Abstract

The $N=4$ supersymmetric self-dual Yang-Mills theory in a four- dimensional space with signature $(2,2)$ is formulated in harmonic superspace. The on-shell constraints of the theory are reformulated in the equivalent form of vanishing curvature conditions for three gauge connections (one harmonic and two space-time). The constraints are then obtained as variational equations from a superspace action of the Chern-Simons type. The action is manifestly $SO(2,2)$ invariant. It can be viewed as the Lorentz-covariant form of the light-cone superfield action proposed by Siegel.