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

TL;DR

This work analyzes the global symmetry structure of two-dimensional NLSMs with a Wess-Zumino term, focusing on isometry and dual isometry symmetries described by two U(1) bundles with curvatures F and F̃. It derives when these symmetries are continuous or discrete, computes their pure and mixed ’t Hooft anomalies, and develops a doubled torus framework to realize T-duality and discrete gauging. The authors show that discrete gauging preserves the symmetry structure under self-duality conditions and construct non-invertible duality defects via half-space gauging, extending known results from the compact boson to general NLSMs. These insights deepen the understanding of non-invertible symmetries in 2D QFTs and pave the way for systematic explorations of new dualities and defect operators in NLSMs.

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.