Nonminimal gradient flows in QCD-like theories

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.

arXiv comment35 pages, accepted for publication

References in corpus (10)

• Properties and uses of the Wilson flow in lattice QCD
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Trivializing maps, the Wilson flow and the HMC algorithm
• Infinite N phase transitions in continuum Wilson loop operators
• Chiral symmetry and the Yang--Mills gradient flow
• The perturbative QCD gradient flow to three loops
• Extended investigation of the twelve-flavor $\beta$-function
• Proof of the renormalizability of the gradient flow
• Testing Fermion Universality at a Conformal Fixed Point
• Dislocations under gradient flow and their effect on the renormalized coupling