Parity Realization in Lattice QCD with Ginsparg-Wilson Fermions

TL;DR

This paper demonstrates that in lattice QCD with Ginsparg-Wilson fermions, parity symmetry remains unbroken in the vacuum when quarks have non-zero mass, contrasting with traditional expectations from continuum theory.

Contribution

It provides a first-principles proof that parity symmetry is realized in lattice QCD with Ginsparg-Wilson fermions for massive quarks, challenging previous assumptions based on continuum arguments.

Findings

Parity order parameters vanish for non-zero quark mass

Ginsparg-Wilson fermions reproduce chiral anomaly correctly

Parity symmetry remains unbroken in the lattice vacuum

Abstract

The Vafa-Witten arguments on the realization of parity and flavour symmetries in the QCD vacuum do not apply to two lattice regularizations of QCD which are able to reproduce the chiral anomaly: Wilson fermions and Ginsparg-Wilson fermions. We show here how using the last regularization one can get, from first principles, that the more standard order parameters for these symmetries take a vanishing vacuum expectation value for any number of flavours, if quarks have a non-vanishing mass.