Symmetries, anomalies, and dualities of two-dimensional Non-Linear Sigma Models

TL;DR

This paper explores the intricate symmetry structures, anomalies, and dualities in two-dimensional Non-Linear Sigma Models with Wess-Zumino terms, revealing how topology influences symmetry types and their anomalies.

Contribution

It provides a detailed analysis of global symmetries, including non-invertible ones, and their anomalies in these models, highlighting the role of topology and dualities.

Findings

Identification of conditions for continuous vs. discrete symmetries

Analysis of 't Hooft anomalies in the models

Construction and invariance of non-invertible symmetries under dualities

Abstract

We analyse the global symmetry structure of two-dimensional Non-Linear Sigma Models with Wess-Zumino term. When the target space has a compact isometry without fixed points, the theory has a pair of (group-like) global symmetries and many such theories also have non-invertible symmetries. We describe how the topology of the target space and Wess-Zumino term determine whether the group-like symmetries are continuous or discrete, and study their pure and mixed 't Hooft anomalies. We also revisit the construction of the non-invertible symmetries, which are associated with possible self-dualities under discrete gauging, and show how the global symmetry structure is left invariant by this gauging.