Recent applications of the Gradient Flow

Loops and Legs in Quantum Field Theory (LL), pp. 062

Abstract

The gradient flow provides a gauge- and O(4)-invariant ultraviolet regulator for QCD. This opens new opportunities for combining non-perturbative lattice calculations with perturbative results, in particular in the context of an operator-product expansion (OPE). We review the concepts behind this and argue that, within the operator basis of a given OPE, the flow-time dependence of the conversion between flowed and regular Wilson coefficients is exact at each perturbative order. Recent applications to parton distribution functions, heavy-meson observables, quark masses, and gradient-flow definitions of the strong coupling are discussed. Finally, the perturbative formulation of the Ricci flow in quantum gravity and its application to the study of non-Gaussian fixed points is reviewed.

Authors 2

1. R. V. Harlander Aachen

   RWTH Aachen University

   Affiliation as printed

   Bayreuth , Germany

   𝑎 RWTH Aachen University , Sommerfeldstr. 16 , 52074 Aachen , Germany

2. A. Shindler