Exact Chiral Symmetry on the Lattice

TL;DR

The paper addresses the long-standing obstruction to lattice chiral symmetry by presenting an overlap-based mechanism that yields exact chirality on the lattice while reproducing continuum anomalies. It develops the theoretical framework (overlap Dirac operator and domain-wall truncations) and demonstrates consistency with perturbative and nonperturbative results, including instanton physics and topological charge on the lattice. By tying the chiral determinant to an overlap of ground states and exploiting the Ginsparg–Wilson relation, the approach enables controlled chiral gauge theories and reliable QCD simulations with exact chiral symmetry. This work has significant implications for lattice QCD and beyond, offering a principled route to exact chirality and correct anomaly structure in nonperturbative settings.

Abstract

Developments during the last eight years have refuted the folklore that chiral symmetries cannot be preserved on the lattice. The mechanism that permits chiral symmetry to coexist with the lattice is quite general and may work in Nature as well. The reconciliation between chiral symmetry and the lattice is likely to revolutionize the field of numerical QCD.