Nonminimal gradient flows in QCD-like theories

TL;DR

This paper extends the Yang-Mills gradient flow in QCD-like theories by incorporating fermionic matter, analyzing different flow equations, and identifying a scheme where fermion anomalous dimensions vanish, with implications for lattice QCD.

Contribution

It introduces a generalized gradient flow including fermions and finds a family of flows with vanishing fermion anomalous dimensions in a specific scheme.

Findings

Identified a one-parameter family of flow systems with vanishing fermion anomalous dimension.

Computed vacuum expectation values and fermion field renormalization up to next-to-leading order.

Studied fermion number dependence and potential applications to lattice QCD.

Abstract

The Yang-Mills gradient flow for QCD-like theories is generalized by including a fermionic matter term in the gauge field flow equation. We combine this with two different flow equations for the fermionic degrees of freedom. The solutions for the different gradient flow setups are used in the perturbative computations of the vacuum expectation value of the Yang-Mills Lagrangian density and the field renormalization factor of the evolved fermions up to next-to-leading order in the coupling. We find a one-parameter family of flow systems for which there exists a renormalization scheme in which the evolved fermion anomalous dimension vanishes to all orders in perturbation theory. The fermion number dependence of different flows is studied and applications to lattice studies are anticipated.