Orbifolds by 2-groups and decomposition

TL;DR

This paper investigates three-dimensional orbifolds by 2-groups with trivial one-form symmetry, demonstrating their decomposition into a disjoint union of theories and interpreting these as sigma models on 2-gerbes.

Contribution

It introduces a framework for understanding orbifolds by 2-groups with trivial one-form symmetry and shows their decomposition into simpler theories, connecting to sigma models on 2-gerbes.

Findings

Orbifolds by 2-groups decompose into disjoint unions of theories.

These theories are sigma models on 2-gerbes.

The formal structure reflects orbifold properties.

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.