Gradient flow and the Wilsonian renormalization group flow

Abstract

The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then illustrate the Wilsonian RG flow on the basis of the gradient flow in two examples that possess an infrared fixed point, the 4D many-flavor gauge theory and the 3D $O(N)$ linear sigma model.

arXiv comment10 pages, 2 figures, the final version to appear in PTEP. Figures 1 and 2 were wrong due to a mistake in the numerical code and have been replaced by corrected ones. We would like to thank Mizuki Tanaka and Masakiyo Kitazawa for pointing out this to us

References in corpus (9)

• Properties and uses of the Wilson flow in lattice QCD
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Trivializing maps, the Wilson flow and the HMC algorithm
• Infinite N phase transitions in continuum Wilson loop operators
• Chiral symmetry and the Yang--Mills gradient flow
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
• The perturbative QCD gradient flow to three loops
• Geometries from field theories
• The Yang-Mills gradient flow and lattice effective action

Cited by in corpus (11)

• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Results and techniques for higher order calculations within the gradient-flow formalism
• Stochastic Renormalization Group and Gradient Flow
• Hadronic vacuum polarization using gradient flow
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• Supersymmetric gradient flow in the Wess-Zumino model
• Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Dynamical solution of the strong CP problem within QCD ?
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• Perturbative analysis of the Wess-Zumino flow