General chiral gauge theories on the lattice

TL;DR

This paper advances the understanding of chiral gauge theories on the lattice by generalizing Dirac operators, analyzing their properties, and exploring correlation functions, gauge invariance, and continuum comparisons.

Contribution

It introduces a broad class of Dirac operators decomposing into Weyl operators and studies their basis representations, correlation functions, and transformation properties.

Findings

General relations for Dirac operators on the lattice

Behavior of correlation functions under gauge and CP transformations

Comparison with continuum perturbation theory

Abstract

We still extend the large class of Dirac operators decribing massless fermions on the lattice found recently, only requiring that such operators decompose into Weyl operators. After deriving general relations and constructions of operators, we study the basis representations of the chiral projections. We then investigate correlation functions of Weyl fermions for any value of the index, stressing the related conditions for basis transformations and their consequences, and getting the precise behaviors under gauge transformations and CP transformations. Various further developments include considerations of the explicit form of the effective action and of a representation of the general correlation functions in terms of alternating multilinear forms. For comparison we also consider gauge-field variations and their respective applications. Finally we compare with continuum perturbation theory.