Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?

TL;DR

This review discusses the challenges and progress in constructing chiral lattice gauge theories through mirror-fermion decoupling, highlighting theoretical issues, toy models, and future research directions.

Contribution

It provides a comprehensive overview of the current status, issues, and potential methods for decoupling mirror fermions in lattice gauge theories, including analysis with Ginsparg-Wilson fermions.

Findings

Mirror-fermion decoupling remains challenging with unresolved issues.

A simple toy model illustrates the desired decoupling features.

Future research directions are identified for advancing the field.

Abstract

This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror-fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the article is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson fermions. We end by pointing out possible directions for future studies.