Properties and uses of the Wilson flow in lattice QCD

TL;DR

This paper explores the Wilson flow in lattice QCD, demonstrating its role in smoothing gauge fields, defining physical quantities, and clarifying topological sector emergence as lattice spacing decreases.

Contribution

It provides a theoretical and numerical analysis of the Wilson flow, highlighting its utility in defining physical observables and understanding topological sectors in lattice QCD.

Findings

Wilson flow produces smooth, renormalized gauge fields at positive flow times.

Expectation values of gauge-invariant expressions are well-defined physical quantities.

Topological sectors become distinguishable as lattice spacing decreases.

Abstract

Theoretical and numerical studies of the Wilson flow in lattice QCD suggest that the gauge field obtained at flow time t>0 is a smooth renormalized field. The expectation values of local gauge-invariant expressions in this field are thus well-defined physical quantities that probe the theory at length scales on the order of sqrt(t). Moreover, by transforming the QCD functional integral to an integral over the gauge field at a specified flow time, the emergence of the topological (instanton) sectors in the continuum limit becomes transparent and is seen to be caused by a dynamical effect that rapidly separates the sectors when the lattice spacing is reduced from 0.1 fm to smaller values.