General chiral gauge theories

TL;DR

This paper explores a broad class of lattice chiral gauge theories by analyzing Dirac operators that decompose into Weyl operators, deriving relations, and examining their gauge and CP transformation properties.

Contribution

It introduces a general framework for chiral gauge theories on the lattice based on spectral properties and detailed structure of chiral projections.

Findings

Derived relations for correlation functions of Weyl fermions.

Established conditions for basis transformations under gauge and CP symmetries.

Presented a determinant form of correlation functions for general cases.

Abstract

Only requiring that Dirac operators decribing massless fermions on the lattice decompose into Weyl operators we arrive at a large class of them. After deriving general relations from spectral representations we study correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and getting the precise behaviors under gauge and CP transformations. Using the detailed structure of the chiral projections we also obtain a form of the correlation functions with a determinant in the general case.