Global Fixed Point Potentials in the Abelian Higgs Model with N flavors
Abstract
Existence of charged fixed points in the Abelian Higgs model with N flavors in d dimensions is studied using the functional renormalization group. We numerically solve the coupled fixed point equations for the scale dependent charge and the non-perturbative effective potential for the scalar field. We show that the ε=4−d expansion, famously successful in theories with O(N) symmetry, fails to produce reliable results when taking the ε→ 1 limit. By determining global fixed point potentials, it is shown that the critical flavor number at which charged fixed points appear, modifies significantly compared to the perturbative treatment. In d=3, signs of a richer fixed point structure with presumably multicritical fixed points are also found. Discussions include subtleties of the gauge fixing and the corresponding modified Ward-Takahashi identities, including the possibility of a nonzero dimensionless photon mass at the infrared fixed point.
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BibTeX
@misc{fejos2026global,
title = {{Global Fixed Point Potentials in the Abelian Higgs Model with $N$ flavors}},
author = {Gergely Fejős and Shunsuke Yabunaka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04938},
eprint = {2609.04938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04938},
}
RIS
TY - UNPB
TI - Global Fixed Point Potentials in the Abelian Higgs Model with N flavors
AU - Gergely Fejős
AU - Shunsuke Yabunaka
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.04938
UR - https://arxiv.org/abs/2609.04938
AB - Existence of charged fixed points in the Abelian Higgs model with N flavors in d dimensions is studied using the functional renormalization group. We numerically solve the coupled fixed point equations for the scale dependent charge and the non-perturbative effective potential for the scalar field. We show that the ε=4−d expansion, famously successful in theories with O(N) symmetry, fails to produce reliable results when taking the ε→ 1 limit. By determining global fixed point potentials, it is shown that the critical flavor number at which charged fixed points appear, modifies significantly compared to the perturbative treatment. In d=3, signs of a richer fixed point structure with presumably multicritical fixed points are also found. Discussions include subtleties of the gauge fixing and the corresponding modified Ward-Takahashi identities, including the possibility of a nonzero dimensionless photon mass at the infrared fixed point.
ER -