Chiral symmetry on the lattice

TL;DR

This paper reviews the challenges of implementing chiral symmetry on the lattice, discussing Wilson Fermions, anomalies, surface modes, mirror Fermions, and implications for lattice Standard Model formulations.

Contribution

It provides a comprehensive overview of the difficulties and approaches related to chiral symmetry in lattice gauge theories, highlighting recent developments and open problems.

Findings

Wilson Fermions near critical hopping parameter exhibit specific chiral properties

Residual chiral symmetry can survive anomalies in multi-flavor cases

Surface mode and mirror Fermion approaches offer potential solutions

Abstract

I review some of the difficulties associated with chiral symmetry in the context of a lattice regulator. I discuss the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. I briefly discuss the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculate on the problems with lattice versions of the standard model.