Anomalies on orbifolds

We review the form of the chiral anomaly on an S1/Z2 orbifold with chiral boundary conditions. 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. We show how to obtain these results in a simple way in terms of the properties of the Kaluza–Klein modes of the orbifold.