Geometrical aspects of chiral anomalies in the overlap

Details Geometrical aspects of chiral anomalies in the overlap Geometrical aspects of chiral anomalies in the overlap

1998-02-25

arxiv.org/abs/hep-lat/9802033v3

Phys.Rev. D59 (1999) 085006

Physics

High Energy Physics

High Energy Physics - Lattice

24 pages, plain TeX, clarifications added

Scientific paper

10.1103/PhysRevD.59.085006

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 dimensional closed sub-manifolds 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.

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