Orbifolds by 2-groups and decomposition

TL;DR

This work develops a framework for 3D orbifolds by 2‑groups with trivially acting BK, showing the theories possess a global 2‑form symmetry and decompose into a disjoint union of theories. The authors formalize a decomposition conjecture: the 3D orbifold QFT on a 2‑group is equivalent to a sum over universes labeled by irreps of K, with each universe corresponding to a G‑orbifold twisted by a discrete theta angle ρ(ω). Partition functions are computed to exhibit the decomposition, via a projector enforcing $x^*ω=1$ and, on suitable manifolds, reducing to discrete‑torsion–like phases $ ho(ω)$. The paper further interprets these theories as sigma models on 2‑gerbes, and discusses higher‑dimensional analogues and CS‑theory counterparts, outlining broad implications for higher‑form symmetries and orbifold constructions. The results illuminate how higher‑form symmetry data controls nonperturbative sectors and the emergence of multiverse structures in 3D QFTs.

Abstract

In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint union of other three-dimensional theories, which we demonstrate. These theories can be interpreted as sigma models on 2-gerbes, whose formal structures reflect properties of the orbifold construction.