Properties and uses of the Wilson flow in lattice QCD

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 0.1fm to smaller values.