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 $SU(3)_C\times SU(3)_L\times SU(3)_R$ 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.