Singular supersymmetric sigma models

TL;DR

This paper investigates the symmetry structure of four-dimensional supersymmetric sigma models with singular metrics, demonstrating that such singularities can be regularized by adding a soft supersymmetry-breaking mass.

Contribution

It introduces a simple anomaly-free extension of the supersymmetric CP^1 model and explores how metric singularities affect the model's symmetry structure.

Findings

Singularities in the Kaehler metric can be regularized with a soft mass parameter.

The regularization preserves the anomaly-free nature of the model.

Insights into the behavior of supersymmetric models with non-invertible metrics.

Abstract

Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure of supersymmetric models in four dimensional space-time in which metric singularities occur. For this purpose we study a simple anomaly-free extension of the supersymmetric CP^1 model from a classical point of view. We show that the metric singularities can be regularized by the addition of a soft supersymmetry-breaking mass parameter.