Anomaly resolution via decomposition

TL;DR

This paper uses decomposition to resolve anomalies in orbifolds with quantum symmetries by enlarging the orbifold group, revealing that such enlargements are equivalent to decomposing into orbifolds by nonanomalous subgroups.

Contribution

It demonstrates that anomaly resolution via group enlargement is equivalent to orbifold decomposition into nonanomalous subgroup orbifolds, providing a general conjecture and examples.

Findings

Enlarged orbifold groups correspond to disjoint unions of nonanomalous orbifolds.

Decomposition shows enlarging the orbifold group is equivalent to reducing it.

The approach offers a new perspective on anomaly resolution in orbifold theories.

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.