Lattice formulation of chiral gauge theories

TL;DR

This paper introduces a comprehensive lattice formulation for chiral gauge theories, expanding the types of Dirac operators and chiral projections possible, while ensuring proper gauge and CP transformation behaviors.

Contribution

It provides a new general framework for chiral gauge theories on the lattice, accommodating broader Dirac spectra and chiral structures with consistent transformation properties.

Findings

Formulation admits Dirac operators with diverse spectra

Correlation functions are valid with zero modes and any index value

Gauge and CP transformation properties are clearly derived

Abstract

We present a general formulation of chiral gauge theories, which admits Dirac operators with more general spectra, reveals considerably more possibilities for the structure of the chiral projections, and nevertheless allows appropriate realizations. In our analyses we use two forms of the correlation functions which both also apply in the presence of zero modes and for any value of the index. To account properly for the conditions on the bases the concept of equivalence classes of pairs of them is introduced. The behaviors under gauge transformations and under CP transformations are unambiguously derived.