Gauging N=2 Supersymmetric Non-Linear $\sigma$-Models in the Atiyah-Ward Space-Time

TL;DR

This paper constructs N=2 supersymmetric non-linear sigma-models within an N=1 superspace framework on Atiyah-Ward space-time, exploring their gauging and gauge-covariant actions in hyper-Kähler target spaces.

Contribution

It introduces a novel class of N=2 supersymmetric sigma-models in (2+2) signature space-time and analyzes their gauging and gauge-covariant formulations.

Findings

Developed N=2 supersymmetric sigma-models in Atiyah-Ward space-time

Presented gauge-covariant supersymmetric action functional

Analyzed gauging of isometries in hyper-Kähler target spaces

Abstract

We build up a class of N=2 supersymmetric non-linear $\sigma$-models in an N=1 superspace based on the Atiyah-Ward space-time of (2+2)-signature metric. We also discuss the gauging of isometries of the associated hyper-K\"ahlerian target spaces and present the resulting gauge-covariant supersymmetric action functional.