Extended Supersymmetry and Self-Duality in 2+2 Dimensions

TL;DR

This paper formulates $N=2$ supersymmetric self-dual Yang-Mills theory and $N=4$ and $N=2$ self-dual supergravities in 2+2 dimensions using superspace solutions, advancing the understanding of supersymmetric theories in non-standard signatures.

Contribution

It provides the first formulations of these self-dual theories in 2+2 dimensions using superspace methods and super-Yang-Mills or supergravity constraints.

Findings

First-time formulation of these theories in 2+2 dimensions.

Utilizes solutions of Bianchi identities in superspace.

Connects self-duality with supersymmetric constraints.

Abstract

The $N=2$ supersymmetric {\it self-dual} Yang-Mills theory and the $N=4$ and $N=2$ {\it self-dual} supergravities in $2+2$ space-time dimensions are formulated for the first time. These formulations utilize solutions of the Bianchi identities subject to the super-Yang-Mills or supergravity constraints in the relevant $N$-extended superspace with the space-time signature $(2,2)$.