Gauge-invariant nonperturbative Wilson action in quantum electrodynamics II
Abstract
The gradient flow exact renormalization group (GFERG) is a formulation of the exact renormalization group for gauge theories that provides a renormalization group flow preserving the gauge Ward--Takahashi identity exactly. In this paper, we nonperturbatively solve the GFERG flow equation for the simplest nontrivial gauge-invariant Wilson action, introduced in a previous paper, for D-dimensional quantum electrodynamics with~Nf flavors (for all~D, flavors are counted in units of four-component spinors). For D=3 and~D=2, a nontrivial infrared fixed point exists even for~Nf=1, and the structure of the critical exponents at the fixed point is qualitatively the same as that in the large-Nf limit. We also obtain the gauge-field propagator in the continuum limit; for~D=2, it reproduces the dynamical mass of the Schwinger model within a few percent. To the best of our knowledge, apart from the large-Nf approximation, this is the first example in which the Wilson renormalization group in a gauge theory is solved nonperturbatively while manifestly preserving gauge symmetry.
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BibTeX
@misc{nagao2026gaugeinvariant,
title = {{Gauge-invariant nonperturbative Wilson action in quantum electrodynamics II}},
author = {Sorato Nagao and Hiroshi Suzuki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19485},
eprint = {2610.19485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19485},
}
RIS
TY - UNPB
TI - Gauge-invariant nonperturbative Wilson action in quantum electrodynamics II
AU - Sorato Nagao
AU - Hiroshi Suzuki
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19485
UR - https://arxiv.org/abs/2610.19485
AB - The gradient flow exact renormalization group (GFERG) is a formulation of the exact renormalization group for gauge theories that provides a renormalization group flow preserving the gauge Ward--Takahashi identity exactly. In this paper, we nonperturbatively solve the GFERG flow equation for the simplest nontrivial gauge-invariant Wilson action, introduced in a previous paper, for D-dimensional quantum electrodynamics with~N_f flavors (for all~D, flavors are counted in units of four-component spinors). For D=3 and~D=2, a nontrivial infrared fixed point exists even for~N_f=1, and the structure of the critical exponents at the fixed point is qualitatively the same as that in the large-N_f limit. We also obtain the gauge-field propagator in the continuum limit; for~D=2, it reproduces the dynamical mass of the Schwinger model within a few percent. To the best of our knowledge, apart from the large-N_f approximation, this is the first example in which the Wilson renormalization group in a gauge theory is solved nonperturbatively while manifestly preserving gauge symmetry.
ER -