Explicit Symmetry Breaking in Non-Abelian Scalar Theories and One-Loop Renormalization
Abstract
Non-Abelian gauge theories coupled to scalar fields are fundamental in particle physics, yet they often face high-energy instabilities. In this work, we start by analyzing the classical SU(2) complex scalar model, mapping the scalar multiplet into a real SO(2N) representation to formalize its generalization to SU(N). Within this classical setup, we introduce an explicit gauge symmetry breaking exclusively in the scalar sector by splitting the mass parameters and quartic self-coupling constants. Moving to the quantum level, we employ the background field method and the Schwinger-DeWitt technique to compute the exact one-loop divergences, explicitly demonstrating the renormalizability of the broken theory. Finally, we derive the Renormalization Group equations and analyze the fixed points of the flow. It is shown that this explicit symmetry breaking asymptotically destabilizes the theory, driving the scalar couplings away from the origin and inevitably leading to a Landau pole.
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BibTeX
@misc{lima2026explicit,
title = {{Explicit Symmetry Breaking in Non-Abelian Scalar Theories and One-Loop Renormalization}},
author = {Lucas Ducastelo de C. C. Lima},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08493},
eprint = {2611.08493},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08493},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explicit Symmetry Breaking in Non-Abelian Scalar Theories and One-Loop Renormalization
AU - Lucas Ducastelo de C. C. Lima
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.08493
UR - https://arxiv.org/abs/2611.08493
AB - Non-Abelian gauge theories coupled to scalar fields are fundamental in particle physics, yet they often face high-energy instabilities. In this work, we start by analyzing the classical SU(2) complex scalar model, mapping the scalar multiplet into a real SO(2N) representation to formalize its generalization to SU(N). Within this classical setup, we introduce an explicit gauge symmetry breaking exclusively in the scalar sector by splitting the mass parameters and quartic self-coupling constants. Moving to the quantum level, we employ the background field method and the Schwinger-DeWitt technique to compute the exact one-loop divergences, explicitly demonstrating the renormalizability of the broken theory. Finally, we derive the Renormalization Group equations and analyze the fixed points of the flow. It is shown that this explicit symmetry breaking asymptotically destabilizes the theory, driving the scalar couplings away from the origin and inevitably leading to a Landau pole.
ER -