Geometrical aspects of chiral anomalies in the overlap

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Abstract
The set of one dimensional lowest energy eigenspaces used to construct the overlap induces a two form on gauge orbit space which is the locally exact curl of Berry’s connection. If anomalies do not cancel, examples of two dimensional closed submanifolds of orbit space are produced over which the integral of the above two form does not vanish. Based on these observations, a natural definition of covariant currents is obtained, a simple way to calculate chiral anomalies on the lattice is found, and indications for how to construct an ideal regularization of chiral gauge theories are seen to emerge.