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.
Highlights
In an orbifold, it is an old story that one has the option of adding modular-invariant phases such as discrete torsion, which in a Γ orbifold are classified by H2(Γ, U(1))
E-mail: dgrobbins@albany.edu, ersharpe@vt.edu, tvandermeulen@albany.edu 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
In appendix A, we review the analogous result for general orbifold groups G, demonstrating that for a quantum symmetry group G = G/[G, G], the orbifold [X/Γ] for Γ = G × Gwith appropriate discrete torsion is equivalent to [X/[G, G]]
Summary
It is an old story that one has the option of adding modular-invariant phases such as discrete torsion, which in a Γ orbifold are classified by H2(Γ, U(1)). It is the purpose of this paper to describe those novel modular-invariant degrees of freedom explicitly These new degrees of freedom generalize quantum symmetries of orbifolds [11, 12], for which reason we use the same nomenclature, and are specific to orbifolds in which a subgroup of the orbifold group acts trivially on the original space. The quantum symmetries we shall be focused on do not always arise from discrete torsion, and so define new modular-invariant phases — but in which the modular invariance is achieved in a novel fashion These new degrees of freedom arise in the case that a subgroup K of the orbifold group Γ acts trivially.
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