A Composite Three-Body-Holonomy Toy Framework for Dynamical Electroweak-Scale Selection
Abstract
We propose a phenomenological toy framework promoted to a minimal three-state internal sector in (3+1) dimensions and realized by composite strong dynamics. It is in a genuine three-body holonomy which originates in a relativistic (1+1)-dimensional Dirac system. The hypothesis is that the number three is not imposed first as a gauge symmetry, but is inherited from the primitive closed cyclic structure of the three-body holonomy. This threefold structure subsequently reappears as a three-state internal space, the three-site loop, a three-flavor hidden sector, and a cubic determinant interaction. We introduce an asymptotically free hidden SU(3)H gauge theory with three Standard-Model-singlet Dirac flavors. Strong hidden dynamics generates a composite condensate, while the inherited holonomy selects its cyclic internal orientation. The anomalous cubic determinant interaction produces a holonomy-dependent potential, and dimensional transmutation generates the characteristic composite scale. The radial composite excitation along the cyclic direction, denoted by S3, couples to the Standard-Model Higgs doublet through a holonomy-dependent CP-even portal. The resulting condensate shifts the Higgs quadratic term and can trigger electroweak symmetry breaking. In the classically scale-invariant reference limit, the electroweak scale is induced from the dynamically generated hidden-sector scale through dimensionless portal couplings.
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BibTeX
@misc{yoshikawa2026composite,
title = {{A Composite Three-Body-Holonomy Toy Framework for Dynamical Electroweak-Scale Selection}},
author = {Tadashi Yoshikawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04202},
eprint = {2610.04202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04202},
}
RIS
TY - UNPB
TI - A Composite Three-Body-Holonomy Toy Framework for Dynamical Electroweak-Scale Selection
AU - Tadashi Yoshikawa
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04202
UR - https://arxiv.org/abs/2610.04202
AB - We propose a phenomenological toy framework promoted to a minimal three-state internal sector in (3+1) dimensions and realized by composite strong dynamics. It is in a genuine three-body holonomy which originates in a relativistic (1+1)-dimensional Dirac system. The hypothesis is that the number three is not imposed first as a gauge symmetry, but is inherited from the primitive closed cyclic structure of the three-body holonomy. This threefold structure subsequently reappears as a three-state internal space, the three-site loop, a three-flavor hidden sector, and a cubic determinant interaction. We introduce an asymptotically free hidden SU(3)_H gauge theory with three Standard-Model-singlet Dirac flavors. Strong hidden dynamics generates a composite condensate, while the inherited holonomy selects its cyclic internal orientation. The anomalous cubic determinant interaction produces a holonomy-dependent potential, and dimensional transmutation generates the characteristic composite scale. The radial composite excitation along the cyclic direction, denoted by S_3, couples to the Standard-Model Higgs doublet through a holonomy-dependent CP-even portal. The resulting condensate shifts the Higgs quadratic term and can trigger electroweak symmetry breaking. In the classically scale-invariant reference limit, the electroweak scale is induced from the dynamically generated hidden-sector scale through dimensionless portal couplings.
ER -