Non-Invertible Symmetry Webs

TL;DR

This paper develops a comprehensive framework for understanding non-invertible symmetries in quantum field theories, focusing on gauging procedures, symmetry webs, and their categorical structures, especially in 3d gauge theories with orthogonal groups.

Contribution

It introduces the concept of non-invertible symmetry webs through sequential partial gaugings and connects these to fusion 2-categories, providing explicit constructions for various groups.

Findings

Complete symmetry web for 3d pure gauge theories with orthogonal groups

Connection between symmetry webs and fusion 2-categories

Extensions proposed for higher-dimensional theories

Abstract

Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The starting point of our analysis is a theory with $G$ 0-form symmetry, and we propose a description of sequential partial gaugings of sub-symmetries. The gauging implements the theta-symmetry defects of the companion paper [1]. The resulting network of symmetry structures related by this gauging will be called a non-invertible symmetry web. Our formulation makes direct contact with fusion 2-categories, and we uncover numerous interesting structures such as symmetry fractionalization in this categorical setting. The complete symmetry web is derived for several groups $G$, and we propose extensions to higher dimensions. The highlight of this analysis is the complete categorical symmetry web, including non-invertible symmetries, for 3d pure gauge theories with orthogonal gauge groups and its extension to arbitrary dimensions.