Non-Linear Supersymmetric $\sigma $-Models and their Gauging in the Atiyah-Ward Space-Time

TL;DR

This paper constructs a supersymmetric non-linear sigma-model within Atiyah-Ward space-time, revealing a specific Kähler manifold structure and implementing gauging of isometries directly in superspace.

Contribution

It introduces a novel supersymmetric sigma-model in Atiyah-Ward space-time with a restricted Kähler manifold and demonstrates gauging of isometries in superspace.

Findings

Derived a Kähler manifold restricted by a specific potential decomposition

Built a supersymmetric sigma-model in Atiyah-Ward space-time

Successfully gauged isometries within the superspace framework

Abstract

We present a supersymmetric non-linear $\s$-model built up in the $N=1$ superspace of Atiyah-Ward space-time. A manifold of the K\"ahler type comes out that is restricted by a particular decomposition of the K\"ahler potential. The gauging of the $\s$-model isometries is also accomplished in superspace.