Gauge invariant non-perturbative Wilson action in quantum electrodynamics

TL;DR

This paper employs the gradient flow exact renormalization group to study gauge-invariant Wilson actions in quantum electrodynamics, explicitly solving the RG equations and obtaining gauge-invariant critical exponents at IR fixed points.

Contribution

It introduces a gauge-invariant non-perturbative ansatz for the Wilson action and explicitly solves the RG flow equations in large N_f approximation, preserving gauge invariance.

Findings

Gauge invariance is exactly preserved under RG flow.

Explicit solutions for the Wilson action at IR fixed points.

Gauge-invariant critical exponents obtained for D<4.

Abstract

By employing the gradient flow exact renormalization group (GFERG), we study the renormalization group (RG) flow of a manifestly gauge or BRST invariant non-perturbative ansatz of the 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.