TL;DR
This paper reviews orbifold operations in 2D quantum field theories, introduces orbifold groupoids for their composition, and discusses extensions to generalized symmetries and RG flow constraints, with insights from 3D TQFTs.
Contribution
It introduces the concept of orbifold groupoids to systematically understand orbifold compositions in 2D QFTs and explores their extensions and applications.
Findings
Orbifold groupoids effectively describe orbifold operation compositions.
3D Dijkgraaf-Witten TQFTs are instrumental in the analysis.
Extensions to generalized symmetries provide new insights.
Abstract
We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the "Orbifold groupoids" which control the composition of orbifold operations. Three-dimensional TQFT's of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications to constrain RG flows.
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