Regularization of Chiral Gauge Theories

Abstract

We propose a nonperturbative formulation of chiral gauge theories. The method involves a `pre-regulation' of the gauge fields, which may be implemented on a lattice, followed by a computation of the chiral fermion determinant in the form of a functional integral which is regularized in the continuum. Our result for the chiral determinant is expressed in terms of the vector-like Dirac operator and hence can be realized in lattice simulations. We investigate the local and global anomalies within our regularization scheme. We also compare our result for the chiral determinant to previous exact $ζ$-function results. Finally, we use a symmetry property of the chiral determinant to show that the partition function for a chiral gauge theory is real.