Global Aspects of Symmetries in Sigma Models with Torsion

TL;DR

This paper investigates how topological sectors in sigma models with torsion can cause anomalies that hinder the quantum realization of classical symmetries, with the anomaly depending on topological and group action properties.

Contribution

It provides a detailed analysis of the topological origins of anomalies in sigma models with torsion and how they affect symmetry implementation at the quantum level.

Findings

Topological sectors can induce anomalies in sigma models with torsion.

The anomaly depends on the homotopy class of the sector and the group action.

Explicit computation of the anomaly shows its topological nature.

Abstract

It is shown that non-trivial topological sectors can prevent the quantum mechanical implementation of the symmetries of the classical field equations of sigma models with torsion. The associated anomaly is computed, and it is shown that it depends on the homotopy class of the topological sector of the theory and the group action on the sigma model manifold that generates the symmetries of the classical field equations.