Anomalies on Orbifolds

TL;DR

This paper investigates the nature of chiral anomalies on S1/Z2 orbifolds, revealing that anomalies are localized on fixed planes and are unaffected by zero mode shape, ensuring consistency of higher-dimensional theories.

Contribution

It demonstrates that the higher-dimensional anomaly is confined to orbifold fixed planes and remains independent of zero mode profiles, linking 4D anomaly cancellation to higher-dimensional consistency.

Findings

Anomaly is localized on orbifold fixed planes.

Higher-dimensional divergence of current is independent of zero mode shape.

4D anomaly cancellation guarantees higher-dimensional consistency.

Abstract

We discuss the form of the chiral anomaly on an S1/Z2 orbifold with chiral boundary conditions. We find that the 4-divergence of the higher-dimensional current evaluated at a given point in the extra dimension is proportional to the probability of finding the chiral zero mode there. Nevertheless the anomaly, appropriately defined as the five dimensional divergence of the current, lives entirely on the orbifold fixed planes and is independent of the shape of the zero mode. Therefore long distance four dimensional anomaly cancellation ensures the consistency of the higher dimensional orbifold theory.