Sorato Nagao | Searcharxiv

arXiv2026

Gauge-invariant nonperturbative Wilson action in quantum electrodynamics

By employing the gradient flow exact renormalization group (GFERG), we study the renormalization group (RG) flow of a manifestly gauge- or Becchi--Rouet--Stora--Tyutin (BRST)-invariant nonperturbative ansatz of the one-particle irreducible (1PI) Wilson action in quantum electrodynamics. The gauge invariance of the Wilson action is \emph{exactly\/} preserved under the RG flow. We explicitly solve the GFERG equation in the leading and partially next-to-leading orders of the large-$N_f$ approximation, where $N_f$ is the number of flavors. We obtain gauge-invariant critical exponents and the gauge-invariant 1PI Wilson action at an infrared (IR) fixed point for~$D<4$, where $D$ is the spacetime dimension.

hep-th↗

arXiv2025

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

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 Lüscher and Weisz, we also argue that GFERG reproduces the conventional renormalization group functions in all orders of perturbation theory.

hep-th↗