A Remark on the Geometry of Two-Dimensional Anisotropic Non-Linear Sigma-Models

TL;DR

This paper explores the geometric structures underlying two-dimensional anisotropic non-linear sigma-models, focusing on gauge anomalies and connections with torsion, especially in non-symmetric coset spaces with anisotropic features.

Contribution

It provides new insights into the geometric conditions related to gauge anomalies and torsion connections in anisotropic sigma-models on non-symmetric coset spaces.

Findings

Connection with torsion affects Ricci tensor properties.

Anisotropy influences the geometric structure of the target manifold.

Gauge anomalies relate to specific geometric configurations.

Abstract

One discusses here the connection between \sigma-model gauge anomalies and the existence of a connection with torsion that does not flatten the Ricci tensor of the target manifold, by considering a number of non-symmetric coset spaces. The influence of an eventual anisotropy on a certain direction of the target manifold is also contemplated.