Anomaly resolution via decomposition

TL;DR

The paper develops and tests a decomposition-based framework for resolving anomalies in orbifolds with quantum symmetries. By embedding the anomalous group G into a central extension Γ and selecting a quantum symmetry B with d2 B = α, the authors show the resulting theory is equivalent to disjoint unions of orbifolds by nonanomalous subgroups, effectively replacing enlargement with a smaller, anomaly-free description. They provide a general conjecture and verify it through detailed examples, including cyclic groups and products such as Z2 × Z2, extended to D4 and H, and a Z2 case extended to Z2 × Z2. The work clarifies how decomposition, quantum symmetries, and discrete torsion interplay to resolve anomalies and unifies several prior perspectives on anomalous orbifolds.

Abstract

In this paper we apply decomposition to orbifolds with quantum symmetries to resolve anomalies. Briefly, it has been argued by e.g. Wang-Wen-Witten, Tachikawa that an anomalous orbifold can sometimes be resolved by enlarging the orbifold group so that the pullback of the anomaly to the larger group is trivial. For this procedure to resolve the anomaly, one must specify a set of phases in the larger orbifold, whose form is implicit in the extension construction. There are multiple choices of consistent phases, which give rise to physically distinct resolutions. We apply decomposition, and find that theories with enlarged orbifold groups are equivalent to (disjoint unions of copies of) orbifolds by nonanomalous subgroups of the original orbifold group. In effect, decomposition implies that enlarging the orbifold group is equivalent to making it smaller. We provide a general conjecture for such descriptions, which we check in a number of examples.