Quantum symmetries in orbifolds and decomposition

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.

LaTeX, 62 pages

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• Combinatoric topological string theories and group theory algorithms
• Decomposition in Chern-Simons theories in three dimensions
• Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
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