Toward a Three-Body Holonomy Standard Model
Abstract
We propose a phenomenological framework toward a Three-Body Holonomy Standard Model in which the number three is selected by the minimal primitive cyclic structure of a democratic many-body interaction network. The resulting threefold holonomy information is assumed to survive in (3+1) dimensions as an internal three-state space. A Lorentz-invariant six-fermion interaction provides a candidate microscopic origin of the internal cyclic correlations, with their matching to Wilson holonomy left as a dynamical requirement. The parity-related holonomy sectors of the underlying (1+1)-dimensional Dirac system motivate left- and right-handed internal structures and a trinification-like SU(3)C× SU(3)L× SU(3)R gauge completion. Vertical holonomy selects a 2+1 splitting, while spontaneous left-right vacuum misalignment provides a possible route to chiral symmetry breaking. Horizontal holonomy organizes the three-family mass structure, with heavy-fermion mixing generating effective flavor and CP-violating patterns. Although a complete ultraviolet derivation remains open, the framework provides a unified scenario connecting primitive three-body dynamics to gauge symmetry, symmetry breaking, and fermion flavor.
Related
- Three-Body Holonomy and SU(3)→ SU(2)× U(1) Symmetry Breaking
- A Composite Three-Body-Holonomy Toy Framework for Dynamical Electroweak-Scale Selection
- Three-Body Holonomy as a Toy-Model Mechanism for Family Triplication and Mass Hierarchy in (1+1) Dimensions
- Thermal masses in the Standard Model at three loops
- Search for physics beyond the standard model in four and three top quark production events using proton-proton collisions at √s = 13 TeV
BibTeX
@misc{yoshikawa2026toward,
title = {{Toward a Three-Body Holonomy Standard Model}},
author = {Tadashi Yoshikawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41175},
eprint = {2610.41175},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41175},
}
RIS
TY - UNPB
TI - Toward a Three-Body Holonomy Standard Model
AU - Tadashi Yoshikawa
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41175
UR - https://arxiv.org/abs/2610.41175
AB - We propose a phenomenological framework toward a Three-Body Holonomy Standard Model in which the number three is selected by the minimal primitive cyclic structure of a democratic many-body interaction network. The resulting threefold holonomy information is assumed to survive in (3+1) dimensions as an internal three-state space. A Lorentz-invariant six-fermion interaction provides a candidate microscopic origin of the internal cyclic correlations, with their matching to Wilson holonomy left as a dynamical requirement. The parity-related holonomy sectors of the underlying (1+1)-dimensional Dirac system motivate left- and right-handed internal structures and a trinification-like SU(3)_C× SU(3)_L× SU(3)_R gauge completion. Vertical holonomy selects a 2+1 splitting, while spontaneous left-right vacuum misalignment provides a possible route to chiral symmetry breaking. Horizontal holonomy organizes the three-family mass structure, with heavy-fermion mixing generating effective flavor and CP-violating patterns. Although a complete ultraviolet derivation remains open, the framework provides a unified scenario connecting primitive three-body dynamics to gauge symmetry, symmetry breaking, and fermion flavor.
ER -