Perturbative analysis of the gradient flow in non-abelian gauge theories

By M. Luscher, Peter Weisz. 2011

382 citations recorded by the source corpus.

The gradient flow in non-abelian gauge theories on $ {\mathbb{R}^4} $ is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner. Similarly to the case of the Langevin equation, the correlation functions of the time-dependent field can be expanded in perturbation theory, the Feynman rules being those of a renormalizable field theory on $ {\mathbb{R}^4} \times \left[ {0,\infty } \right) $. For any matter multiplet and to all loop orders, we show that the correlation functions are finite, i.e. do not require additional renormalization, once the theory in four dimensions is renormalized in the usual way. The flow thus maps the gauge field to a one-parameter family of smooth renormalized fields.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f1acac8e1ed77b72f7e4f967591faae06b92817a

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Citations in the corpus

FLAG Review 2019 (2019, background): “The field at finite flow time can be shown to be renormalized [1075].”
High-precision scale setting in lattice QCD (2012, methodology): “In [12, 13], where the Wilson action is used, Z(Vt) is the derivative of the plaquette action and the corresponding flow is called the Wilson flow.”
A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results (2018, background): “[199], it defines a 4+1-dimensional field theory, wherein the extra dimension is the flow time.”
Simulation of QCD with Nf = 2 + 1 flavors of non-perturbatively improved Wilson fermions (2014, methodology): “The Wilson flow can be a very useful tool in lattice QCD from which quantities with a finite continuum limit can be constructed [6, 56, 57].”
Scale Setting in Lattice QCD (2014, methodology): “The proof of finiteness to all orders of perturbation theory uses a formulation in terms of a 5-dimensional theory, adding the extra dimension t (with dimension length2) and a boundary t = 0 [31].”