Anomalies on Six Dimensional Orbifolds

TL;DR

This paper analyzes localized gauge and gravitational anomalies in six-dimensional Z_n orbifolds, providing a simple formula for bulk fermion contributions and discussing anomaly cancellation mechanisms including Green-Schwarz forms and localized fermions.

Contribution

It introduces a simple, n-independent expression for bulk fermion anomaly contributions and explores anomaly cancellation via localized fermions and Green-Schwarz forms in six-dimensional orbifolds.

Findings

Bulk fermion anomaly contribution is independent of orbifold twist order.

Anomalies can be canceled by localized fermions and Green-Schwarz forms.

Localized gravitational anomalies require nontrivial localized fields.

Abstract

We consider localized anomalies in six dimensional Z_n orbifolds. We give a very simple expression for the contribution of a bulk fermion to the fixed point gauge anomaly that is independent of the order n of the orbifold twist. We show it can be split into three terms, two of which are canceled by bulk fermions and Green-Schwarz four forms respectively. The remaining anomaly carries an integer coefficient and hence can be canceled by localized fermions in suitable representations. We present various examples in the context of supersymmetric theories. Also we point out that the six-dimensional gravitational symmetries generally have localized anomalies that require localized four-dimensional fields to transform nontrivially under them.