Chiral Fermions on the Lattice

TL;DR

This paper reviews the development of a lattice formulation that preserves chiral symmetry exactly, enabling non-perturbative studies of QCD and related theories with well-defined topological charge.

Contribution

It introduces a modified lattice chiral symmetry formulation that overcomes longstanding regularization issues for chiral fermions.

Findings

Exact chiral symmetry on the lattice established

Application to QCD in various regimes demonstrated

Relation to Random Matrix Theory and Chiral Perturbation Theory shown

Abstract

In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This also provides a sound definition of the topological charge of lattice gauge configurations. We illustrate a variety of applications to QCD in the p-, the epsilon- and the delta-regime, where simulation results can now be related to Random Matrix Theory and Chiral Perturbation Theory. The latter contains Low Energy Constants as free parameters, and we comment on their evaluation from first principles of QCD.