Geometrical aspects of chiral anomalies in the overlap - art. no. 085006

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 dim ensional closed submanifolds of orbit space are produced over which the int egral of the above two form does not vanish. Based on these observations, a natural definition of covariant currents is obtained, a simple way to calc ulate chiral anomalies on the lattice is found, and indications for how to construct an ideal regularization of chiral gauge theories an seen to emerg e. [S0556-2821(99)00808-5].