Axial Anomaly for Eguchi-Hanson Metrics with Nonzero Total Mass

We compute the Dirac indexes for the two spin structures κ0 and κ1 for Eguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish in general, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes for the spin structure κ0, and no axial anomaly exists in this case.