Gradient flow and the Wilsonian renormalization group flow

TL;DR

This paper explores the relationship between gradient flow and Wilsonian renormalization group flow, illustrating their connection through examples like the 4D gauge theory and 3D sigma model, highlighting their fixed points.

Contribution

It provides a simple argument linking gradient flow to Wilsonian RG flow and demonstrates this connection with concrete examples involving infrared fixed points.

Findings

Gradient flow relates to Wilsonian RG flow.

Illustrated connection in 4D gauge theory with many flavors.

Demonstrated in 3D O(N) linear sigma model.

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.