Quantum symmetries in orbifolds and decomposition

TL;DR

This paper introduces new modular-invariant phase factors for orbifolds, generalizing quantum symmetries and discrete torsion, and proposes a decomposition framework relating these orbifolds to simpler disjoint unions.

Contribution

It develops a novel set of phase factors for orbifolds with trivially-acting subgroups and extends the decomposition principle to include these new phases.

Findings

New phase factors are modular-invariant and generalize discrete torsion.

Decomposition relates complex orbifolds with these phases to simpler disjoint unions.

Numerical examples confirm the proposed equivalences.

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.