Properties and uses of the Wilson flow in lattice QCD

By M. Luscher. 2010

593 citations recorded by the source corpus.

: 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 √ 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.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f5f85774a6d0377c6f793bf7f368ca3da994d2a6

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Citations in the corpus

Lattice QCD without topology barriers (2011, methodology): “the sectors” decreases with a high power of the lattice spacing [1].”
Perturbative analysis of the gradient flow in non-abelian gauge theories (2011, background): “[1,2], the gradient flow provides further opportunities to probe these theories and allows some of their otherwise elusive properties to be understood (in lattice gauge theory, the gradient flow is referred to as the Wilson flow, while in the mathematical literature it is commonly known as the Yang–”
Simulation of QCD with Nf = 2 + 1 flavors of non-perturbatively improved Wilson fermions (2014, methodology): “However, with the advent of the gradient flow in lattice computations [5, 6] it has been discovered that at moderate lattice spacing other quantities constructed from smoothed fields evolve even slower in Monte Carlo time [7, 8].”
Scale Setting in Lattice QCD (2014, background): “First I define the scales [30, 33] t0 : E (t0) = 0.”
High-precision scale setting in lattice QCD (2012, methodology): “Its application to scale setting, which we build upon, was suggested recently in [12].”
Critical slowing down and error analysis in lattice QCD simulations (2010, background): “Martin Lüscher investigated observables after integrating the Wilson flow [30] for some distance which removes UV fluctuations.”
Setting the scale for the CLS 2 +1 flavor ensembles (2016, unknown): “[2] using the Wilson flow.”
Review of lattice results concerning low-energy particle physics (2016, methodology): “Furthermore, we may expect a significant reduction of errors due to new definitions of running couplings [591,592] using the Yang Mills gradient flow [245].”
The Yang-Mills gradient flow in finite volume (2012, background): “DN would like to thank Kalman Szabo for suggesting to look into [3] for possible applications and also Pierre van Baal for very useful discussions and correspondence during the past 10 years on the small volume expansion of gauge theories.”