Chiral Extension of Lattice Gauge Theory

TL;DR

This paper introduces two novel methods for coupling Goldstone modes to massless quarks on the lattice, maintaining exact chiral symmetry, with potential implications for lattice QCD simulations.

Contribution

It presents two new approaches to incorporate Goldstone modes into lattice gauge theory while preserving chiral symmetry, expanding the toolkit for lattice QCD.

Findings

First approach generalizes XQCD consistent with Ginsparg-Wilson relation.

Second approach uses coset construction with real determinant at zero axial coupling.

Both methods maintain exact chiral symmetry on the lattice.

Abstract

Two approaches are presented to coupling explicit Goldstone modes to $N_f$ flavors of massless quarks preserving exact $SU(N_f) \times SU(N_f)$ chiral symmetry on the lattice. The first approach is a generalization a chiral extension to QCD (aka XQCD) proposed by Brower, Shen and Tan consistent with the Ginsparg-Wilson relation. The second approach based on the Callan,Coleman, Wess and Zumino coset construction has a real determinant atzero quark axial coupling, $g_A = 0$.