Geometric-Algebraic Unification of Fundamental Interactions: From Higgs Mechanism to Quark Confinement via Torsion

This paper presents a novel unified theory of fundamental interactions based on a geometric-algebraic framework. The theory extends the Einstein-Cartan formalism by introducing algebraic constraints that couple torsion to gauge field strengths through orthogonal imaginary operators. The model naturally incorporates the Standard Model gauge groups via a direct sum of Clifford algebras, with fermions emerging as minimal ideals. The Higgs mechanism is geometrized through its coupling to torsion, providing a new perspective on mass generation. Most notably, quark confinement is explained as a geometric phenomenon where gluon fields create torsion tubes that yield linearly rising potentials. The theory predicts testable modifications to Higgs decays, gravitational wave propagation in presence of Higgs condensates, and new effects in quark-gluon plasma. All fundamental equations—Einstein-Cartan, Yang-Mills, Dirac, and Higgs—are derived from a single variational principle.