Reflection positive formulation of chiral gauge theories on a lattice

TL;DR

This paper develops a lattice formulation for gauge invariant chiral theories that satisfy reflection positivity, utilizing half gauge fields, and demonstrates the approach with a detailed two-dimensional model.

Contribution

It introduces a reflection positive lattice formulation of chiral gauge theories using half gauge fields, advancing non-perturbative studies.

Findings

Constructed gauge invariant chiral theories on a lattice

Utilized half gauge fields for reflection positivity

Analyzed a specific two-dimensional model

Abstract

Gauge invariant chiral theories satisfying the reflection positivity is constructed on a lattice. This requires the introduction of "half gauge fields" defined some time ago by Brydges, Fr\"{o}hlich, and Seiler \cite{BFS}. A two-dimensional model is considered in some detail.