Yang--Mills $\beta$ function in the gradient flow exact renormalization group

TL;DR

This paper introduces the GFERG method for Yang--Mills theory, which preserves gauge symmetry and accurately reproduces known renormalization group functions at one-loop and in all orders of perturbation theory.

Contribution

It provides an explicit computation of the one-loop RG functions within GFERG and demonstrates its equivalence to conventional RG functions to all orders.

Findings

GFERG reproduces correct one-loop RG coefficients.

GFERG aligns with the gradient flow formalism.

GFERG reproduces conventional RG functions in all orders.

Abstract

The gradient flow exact renormalization (GFERG) is a variant of the exact renormalization group of gauge theory that aims to preserve gauge symmetry as manifestly as possible. From an integral representation of the Wilson action in GFERG for the Yang--Mills theory, we explicitly compute the one-loop renormalization group functions that reproduce correct coefficients. From the correspondence with the gradient flow formalism by L\"uscher and Weisz, we also argue that GFERG reproduces the conventional renormalization group functions in all orders of perturbation theory.