Anomalies, Extensions and Orbifolds

TL;DR

This paper explores gauge anomalies in orbifold conformal field theories, classifies their origins via cohomology, and proposes methods to extend orbifold groups to eliminate anomalies, supported by explicit examples.

Contribution

It introduces a general method for constructing extensions of orbifold groups to cancel anomalies and tests the conjecture relating these extensions to orbifolds by non-anomalous subgroups.

Findings

Anomalies correspond to failures of modular invariance in orbifold partition functions.

Extending orbifold groups can remove anomalies, guided by cohomological classification.

Consistent extensions are often equivalent to orbifolds by non-anomalous subgroups.

Abstract

We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is classified by cohomology and how extending the orbifold group can remove it. Working with such extensions requires an understanding of the consistent ways in which extending groups can act on the twisted states of the original symmetry, which leads us to a discrete-torsion like choice that exists in orbifolds with trivially-acting subgroups. We review a general method for constructing such extensions and investigate its application to orbifolds. Through numerous explicit examples we test the conjecture that consistent extensions should be equivalent to (in general multiple copies of) orbifolds by non-anomalous subgroups.