The Yang-Mills gradient flow and lattice effective action

Abstract

Recently, the Yang-Mills gradient flow is found to be a useful concept not only in lattice simulations but also in continuous field theories. Since its smearing property is similar to the Wilsoninan "block spin transformation", there might be deeper connection between them. In this work, we define the "effective action" which generates configurations at a finite flow time and derive the exact differential equation to investigate the flow time dependence of the action. Then Yang-Mills gradient flow can be regarded as the flow of the effective action. We also propose the flow time dependent gradient, where the differential equation becomes similar to the renormalization group equation. We discuss a possibility to regard the time evolution of the effective action as the Wilsonian renormalization group flow.

16 pages, 3 figures; accepted for publication in PTEP

References in corpus (4)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Gradient Flow of O(N) nonlinear sigma model at large N

Cited by in corpus (10)

• Gradient flow and the renormalization group
• Derivation of a Gradient Flow from ERG
• Gradient flow and the Wilsonian renormalization group flow
• Stochastic Renormalization Group and Gradient Flow
• Gradient flow exact renormalization group
• Gradient flow exact renormalization group -- inclusion of fermion fields
• Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
• Supersymmetric gradient flow in the Wess-Zumino model
• A basis of the gradient flow exact renormalization group for gauge theory
• Perturbative analysis of the Wess-Zumino flow