Quantum symmetries in orbifolds and decomposition

TL;DR

The paper introduces modular-invariant phase factors for orbifolds with trivially-acting subgroups, extending the concept of quantum symmetries beyond discrete torsion. It proposes a general decomposition conjecture, relating Γ-orbifolds with quantum symmetry B to disjoint unions of simpler orbifolds weighted by Ker B and Coker B, with discrete torsion determined by the extension class. The authors validate the conjecture across a broad array of examples, including cyclic, dihedral, and product groups, using genus-one partition functions as consistency checks and highlighting how dt twists interplay with decomposition. They also discuss open string sector implications, D-brane constructions, and the status of non-central extensions, setting the stage for future work on anomaly resolution and wider applicability. Overall, the work provides a systematic framework for incorporating generalized quantum symmetries into orbifolds and decomposing them into simpler, well-understood theories with precise predictive power.

Abstract

In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we generalize decomposition to include orbifolds with these new phase factors, making a precise proposal for how such orbifolds are equivalent to disjoint unions of other orbifolds without trivially-acting subgroups or one-form symmetries, which we check in numerous examples.