Orbifolds of topological quantum field theories

TL;DR

This paper rigorously explains the orbifold construction in topological quantum field theories, connecting state sum and symmetry gauging perspectives, with examples and implications for full quantum field theories.

Contribution

It clarifies the mathematical understanding of orbifolds in topological QFTs, linking defect-based and symmetry-based approaches, and discusses broader implications.

Findings

Orbifold construction can be viewed as a state sum or symmetry gauging.

Provides rigorous mathematical framework for orbifolds in topological QFTs.

Includes examples illustrating the concepts and potential relevance to full QFT.

Abstract

The orbifold construction via topological defects in quantum field theory can either be understood as a state sum construction internal to a given ambient theory, or as the procedure of (identifying and) gauging ordinary and "non-invertible" symmetries. Here we explain how this is rigorously understood in the case of topological QFTs. We provide various examples and outline general features, also of relevance for full QFT.