One-particle irreducible Wilson action in the gradient flow exact renormalization group formalism

TL;DR

This paper introduces a 1PI Wilson action within the GFERG formalism for QED, demonstrating that the flow preserves conventional gauge and chiral symmetries, which may facilitate non-perturbative studies.

Contribution

It defines a 1PI Wilson action in GFERG formalism and shows the preservation of conventional gauge and chiral symmetries under the flow, contrasting with the original Wilson action.

Findings

GFERG flow preserves conventional U(1) gauge invariance for 1PI Wilson action.

Conventional form of global chiral transformation is maintained.

Potential for non-perturbative ansatz for gauge and chiral invariant actions.

Abstract

We define a one-particle irreducible (1PI) Wilson action in the gradient flow exact renormalization group (GFERG) formalism as the Legendre transform of a Wilson action. We consider quantum electrodynamics in particular, and show that the GFERG flow equation preserves the invariance of the 1PI Wilson action (excluding the gauge-fixing term) under the \emph{conventional\/} $U(1)$ gauge transformation. This is in contrast to the invariance of the original Wilson action under a modified $U(1)$ gauge transformation. The global chiral transformation also takes the \emph{conventional\/} form for the 1PI Wilson action. Despite the complexity of the GFERG flow equation, the conventional form of the gauge and global chiral transformations may allow us to introduce a non-perturbative Ansatz for gauge and chiral invariant 1PI Wilson actions.