Wilsonian exact renormalization group flow in the gauged Nambu--Jona-Lasinio model
Abstract
We study the Wilsonian exact renormalization group flow of the gauged Nambu--Jona-Lasinio (NJL) model, a four-dimensional U(1) gauge theory with chirally invariant four-Fermi interactions, by using the gradient flow exact renormalization group~(GFERG). Our gauge-invariant ansatz (truncation) for the 1PI Wilson action keeps a general photon kinetic function~𝒦τ(k2), the fermion mass, and the scalar and vector four-Fermi couplings. For a fixed gauge coupling~e2, the Gaussian and NJL (quasi-)fixed points on the critical surface merge at~ec2≃17, as anticipated by the ladder Schwinger--Dyson equation and the conventional Wilsonian renormalization group. We then let e2 itself flow. Owing to the manifest gauge invariance of the GFERG, the flow of~e2 is governed solely by the photon anomalous dimension~γA, which remains positive along both branches up to the merging point. Hence, no fixed point with~e2≠0 exists. Flows from a sufficiently large~e2 in the ultraviolet (UV) reach the chirally broken phase even for vanishing four-Fermi couplings, so the gauge interaction does trigger chiral symmetry breaking. The merging point, however, is not a fixed point, and the gauge coupling vanishes in any continuum limit within our truncation.
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BibTeX
@misc{nagao2026wilsonian,
title = {{Wilsonian exact renormalization group flow in the gauged Nambu--Jona-Lasinio model}},
author = {Sorato Nagao and Hiroshi Suzuki},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00559},
eprint = {2611.00559},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00559},
}
RIS
TY - UNPB
TI - Wilsonian exact renormalization group flow in the gauged Nambu--Jona-Lasinio model
AU - Sorato Nagao
AU - Hiroshi Suzuki
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00559
UR - https://arxiv.org/abs/2611.00559
AB - We study the Wilsonian exact renormalization group flow of the gauged Nambu--Jona-Lasinio (NJL) model, a four-dimensional U(1) gauge theory with chirally invariant four-Fermi interactions, by using the gradient flow exact renormalization group~(GFERG). Our gauge-invariant ansatz (truncation) for the 1PI Wilson action keeps a general photon kinetic function~𝒦_τ(k^2), the fermion mass, and the scalar and vector four-Fermi couplings. For a fixed gauge coupling~e^2, the Gaussian and NJL (quasi-)fixed points on the critical surface merge at~e_c^2≃17, as anticipated by the ladder Schwinger--Dyson equation and the conventional Wilsonian renormalization group. We then let e^2 itself flow. Owing to the manifest gauge invariance of the GFERG, the flow of~e^2 is governed solely by the photon anomalous dimension~γ_A, which remains positive along both branches up to the merging point. Hence, no fixed point with~e^2≠0 exists. Flows from a sufficiently large~e^2 in the ultraviolet (UV) reach the chirally broken phase even for vanishing four-Fermi couplings, so the gauge interaction does trigger chiral symmetry breaking. The merging point, however, is not a fixed point, and the gauge coupling vanishes in any continuum limit within our truncation.
ER -