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.
Highlights
Decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories
Decomposition was first introduced in [8] to understand orbifolds and two-dimensional gauge theories in which a finite subgroup of the gauge group acts trivially on the theory. (If the subgroup is abelian, this means that the theory has a finite global one-form symmetry, in modern language, but decomposition is defined more generally.) Briefly, decomposition says that such a quantum field theory is equivalent to (’decomposes’ into) a disjoint union of related quantum field theories, often constructed from orbifolds and gauge theories by effectively-acting quotients of the original gauge group
The original work on decomposition [8] studied orbifolds and gauge theories, but did not consider orbifolds in which discrete torsion was turned on in a way that obstructed the existence of the one-form symmetry, except to note that the decomposition story did not apply to such cases
Summary
Orbifolds, see e.g. [1,2,3,4,5,6,7], utilizing new methods and insights into anomalies from topological defect lines and related technologies, and. (If the subgroup is abelian, this means that the theory has a finite global one-form symmetry, in modern language, but decomposition is defined more generally.) Briefly, decomposition says that such a quantum field theory is equivalent to (’decomposes’ into) a disjoint union of related quantum field theories, often constructed from orbifolds and gauge theories by effectively-acting quotients of the original gauge group. After this paper appeared on the arXiv, we learned of [34] which discusses decomposition in the presence of B fields and derives similar conclusions, albeit from a different computational perspective
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