A generalization of decomposition in orbifolds

TL;DR

This paper extends the concept of decomposition in orbifolds to cases involving discrete torsion, showing that even when traditional decomposition is broken, remnants of it persist, with implications for gauge theories and quantum symmetries.

Contribution

It generalizes the decomposition framework in orbifolds to include discrete torsion cases, broadening understanding of orbifold gauge theories.

Findings

Decomposition can be generalized to orbifolds with discrete torsion.

Remnants of decomposition are observed even when broken.

Includes quantum symmetries of abelian orbifolds as special cases.

Abstract

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds.