Yang–Mills <i>β</i> Function in the Gradient Flow Exact Renormalization Group

Abstract The gradient flow exact renormalization group (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 the correct coefficients. From the correspondence with the gradient flow formalism by Lüscher and Weisz (J. High Energy Phys. 1102, 051 (2011)), we also argue that GFERG reproduces the conventional renormalization group functions in all orders of perturbation theory.