The Geometry of N=1 and N=2 Real Supersymmetric Non-Linear Sigma-Models in the Atiyah-Ward Space-Time

TL;DR

This paper explores the geometric structures of N=1 and N=2 supersymmetric non-linear sigma-models in Atiyah-Ward space-time, revealing new features like locally product structures and split-quaternionic automorphisms.

Contribution

It introduces novel geometric structures in supersymmetric sigma-models, including locally product structures for N=1 and split-quaternionic automorphisms for N=2 cases.

Findings

Discovery of locally product structure in N=1 models

Identification of split-quaternionic automorphisms in N=2 models

New geometric features in supersymmetric sigma-models

Abstract

We analyse the structure of N=1 and N=2 supersymmetric non-linear sigma-models built up with a pair of real superfields defined in the superspace of Atiyah-Ward space-time. The geometry arising has new features such as the existence of a locally product structure (N=1 case) and a set of automorphisms of the tangent space that is isomorphic to the split-quaternionic algebra (N=2 case).