2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging

TL;DR

This paper investigates 2-group symmetries in 3D topological quantum field theories, exploring conditions for gauging these symmetries and their implications for constructing new TQFTs, especially in the context of Reshetikhin-Turaev theories.

Contribution

It provides a framework for gauging 2-group symmetries in 3D TQFTs and analyzes their effects in theories derived from G-crossed braided fusion categories.

Findings

Gauging of symmetries is possible when defects satisfy orbifold data axioms.

Gauging the 0-form G-symmetry yields the equivariantisation of the category.

For commutative G, the symmetry reduces to a 1-form symmetry involving the Pontryagin dual.

Abstract

A large class of symmetries of topological quantum field theories is naturally described by functors into higher categories of topological defects. Here we study 2-group symmetries of 3-dimensional TQFTs. We explain that these symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data. In the special case of Reshetikhin-Turaev theories coming from $G$-crossed braided fusion categories $\mathcal C^\times_G$, we show that there are 0- and 1-form symmetries which have no obstructions to gauging. We prove that gauging the 0-form $G$-symmetry on the neutral component $\mathcal C_e$ of $\mathcal C^\times_G$ produces its equivariantisation $(\mathcal C^\times_G)^G$, which in turn features a generalised symmetry whose gauging recovers $\mathcal C_e$. If $G$ is commutative, the latter symmetry reduces to a 1-form symmetry involving the Pontryagin dual group.