Gradient flow exact renormalization group -- inclusion of fermion fields

TL;DR

This paper extends the gradient flow exact renormalization group framework to include fermion fields in gauge theories, maintaining gauge invariance and exploring chiral symmetry options, with a perturbative application to QED.

Contribution

The authors generalize GFERG to fermionic gauge theories, preserving gauge invariance and analyzing chiral symmetry formulations, with explicit perturbative results in QED.

Findings

Constructed a gauge-invariant Wilson action in QED.

Reproduced the axial anomaly correctly in two dimensions.

Compared two chiral symmetry formulations within GFERG.

Abstract

The gradient flow exact renormalization group (GFERG) is an exact renormalization group motivated by the Yang--Mills gradient flow and its salient feature is a manifest gauge invariance. We generalize this GFERG, originally formulated for the pure Yang--Mills theory, to vector-like gauge theories containing fermion fields, keeping the manifest gauge invariance. For the chiral symmetry we have two options: one possible formulation preserves the conventional form of the chiral symmetry and the other simpler formulation realizes the chiral symmetry in a modified form \`a la Ginsparg--Wilson. We work out a gauge-invariant local Wilson action in quantum electrodynamics to the lowest nontrivial order of perturbation theory. This Wilson action reproduces the correct axial anomaly in~$D=2$.