Uses of Sigma Models

TL;DR

This paper reviews various applications of nonlinear sigma models, emphasizing their role in probing target space geometries and exploring connections with supersymmetry and complex geometries.

Contribution

It provides a comprehensive overview of sigma models' uses, especially in relation to supersymmetric theories and complex geometric structures.

Findings

Sigma models serve as tools to study target space geometries.

Supersymmetric sigma models relate to Kähler and hyperkähler geometries.

The review highlights the connection between sigma models and advanced geometric frameworks.

Abstract

This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to K\"ahler, hyperk\"ahler, hyperk\"ahler with torsion and generalised K\"ahler geometries is described.