Journal of High Energy Physics

, 2011:51 | Cite as

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

  • Martin LüscherEmail author
  • Peter Weisz
Open Access


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.


Lattice QCD Lattice Gauge Field Theories Renormalization Regularization and Renormalons Field Theories in Higher Dimensions 


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© The Author(s) 2011

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.CERN, Physics DepartmentGeneva 23Switzerland
  2. 2.Max-Planck-Institut für PhysikMunichGermany

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