Functional Renormalization Group Flows and Gauge Consistency in QED

TL;DR

This paper develops a systematic expansion scheme within the functional renormalization group framework to find gauge-consistent solutions in quantum electrodynamics with four-Fermi interactions, analyzing phase structure numerically.

Contribution

It introduces a method ensuring solutions satisfy the quantum master equation, advancing gauge consistency in non-perturbative RG analyses of QED.

Findings

Gauge and four-Fermi couplings' phase structure analyzed

Numerical solutions demonstrate gauge consistency in lowest order truncation

Framework applicable to non-perturbative gauge theories

Abstract

We consider quantum electrodynamics with chiral four-Fermi interactions in the functional renormalization group approach. In gauge theories, the functional flow equation for the effective action is accompanied by the quantum master equation that governs the underlying gauge symmetry. Beyond perturbation theory, fully gauge-consistent solutions are very difficult to obtain. We devise a systematic expansion scheme in which the solutions of the flow equation also solve the Quantum Master Equation. In the present work we apply this construction within the lowest order corrections in the photon two-point functions. In this truncation we discuss the phase structure in terms of the gauge and four-Fermi couplings based on a numerical solution of the system.