Exact Solutions for Self--Dual Yang--Mills and Self--Dual Tensor Multiplets on Gravitational Instanton Background

TL;DR

This paper presents the first exact solutions for coupled self-dual Yang-Mills and tensor multiplets in a supersymmetric setting on gravitational instanton backgrounds, with implications for integrable models and superstring theory.

Contribution

It provides the first explicit solutions for N=1 supersymmetric self-dual multiplets in (2+2) dimensions on Eguchi-Hanson backgrounds, using a novel method from known self-dual gravity solutions.

Findings

Exact solutions for self-dual Yang-Mills and tensor multiplets on Eguchi-Hanson background.

Method to derive Yang-Mills solutions from self-dual gravity solutions.

Analysis of solution consistency as backgrounds for N=2 superstring.

Abstract

We give exact solutions for a recently developed ~$N=1$~ locally supersymmetric self-dual gauge theories in $~(2+2)\-$dimensions. We give the exact solutions for an $~SL(2)$~ self-dual Yang-Mills multiplet and what we call ``self-dual tensor multiplet'' on the gravitational instanton background by Eguchi-Hanson. We use a general method to get an $~SL(2)$~ self-dual Yang-Mills solution from any known self-dual gravity solution. Our result is the first example of exact solutions for the coupled system of these $~N=1$~ locally supersymmetric self-dual multiplets in ~$(2+2)\-$dimensions, which is supposed to have strong significance for integrable models in lower-dimensions upon appropriate dimensional reduction or truncation. We also inspect the consistency of our exact solutions as a background for $~N=2$~ superstring coupled to the Wess-Zumino-Witten term in $~\s\-$model formulation.