Nonlinear Realization of Chiral Symmetry on the Lattice

TL;DR

This paper introduces a lattice formulation where chiral symmetry is nonlinearly realized, allowing for exact symmetry preservation while removing fermion doublers, enabling non-perturbative studies of baryons and quarks interacting with pions.

Contribution

The authors develop a novel lattice approach with nonlinear chiral symmetry realization that maintains symmetry with Wilson terms and facilitates non-perturbative QCD studies.

Findings

Chiral symmetry is preserved without breaking by fermion mass terms.

The formulation allows lattice studies of baryons at non-zero density.

It provides a way to test the validity of the chiral quark model in QCD.

Abstract

We formulate lattice theories in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework the fermion mass term does not break chiral symmetry. This property allows us to use the Wilson term to remove the doubler fermions while maintaining exact chiral symmetry on the lattice. Our lattice formulation enables us to address non-perturbative questions in effective field theories of baryons interacting with pions and in models involving constituent quarks interacting with pions and gluons. We show that a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering complex action problems. In our formulation one can also decide non-perturbatively if the chiral quark model of Georgi and Manohar provides an appropriate low-energy description of QCD. If so, one could understand why the non-relativistic quark model works.