Gradient Flow: Perturbative and Non-Perturbative Renormalization

Abstract

We review the gradient flow for gauge and fermion fields and its applications to lattice gauge theory computations. Using specific examples, we discuss the interplay between perturbative and non-perturbative calculations in the context of renormalization with the gradient flow.

12 pages, 3 figures, review presented at the XVth "Quark confinement and the Hadron spectrum" conference. This version fixes few typos of the published version

References in corpus (13)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• The strong coupling from a nonperturbative determination of the $\Lambda$ parameter in three-flavor QCD
• The lattice gradient flow at tree-level and its improvement
• Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• The perturbative QCD gradient flow to three loops
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Short flow-time coefficients of CP-violating operators
• Four quark operators for kaon bag parameter with gradient flow
• Large-$N$ limit of the gradient flow in the 2D $O(N)$ nonlinear sigma model
• Non-perturbative QCD: renormalization, O(a)-improvement and matching to Heavy Quark Effective Theory
• On the chiral anomaly and the Yang-Mills gradient flow

Cited by in corpus (1)

• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow