Chiral symmetry and the Yang--Mills gradient flow

TL;DR

This paper extends the Yang--Mills gradient flow to quark fields in QCD, enabling non-perturbative studies of gauge theories with applications in lattice QCD for renormalization and precise calculations.

Contribution

It introduces a simple extension of the gradient flow to quark fields, establishing its renormalizability and broadening its applications in lattice QCD.

Findings

Renormalizability of correlation functions with local fields at positive flow times.

Application in non-perturbative renormalization and O(a) improvement.

Accurate calculations of chiral condensate and pseudo-scalar decay constant.

Abstract

In the last few years, the Yang--Mills gradient flow was shown to be an attractive tool for non-perturbative studies of non-Abelian gauge theories. Here a simple extension of the flow to the quark fields in QCD is considered. As in the case of the pure-gauge gradient flow, the renormalizability of correlation functions involving local fields at positive flow times can be established using a representation through a local field theory in 4+1 dimensions. Applications of the extended flow in lattice QCD include non-perturbative renormalization and O(a) improvement as well as accurate calculations of the chiral condensate and of the pseudo-scalar decay constant in the chiral limit.