Geometric Confinement from Torsion Flux Tubes: An Algebraic Unification of QCD and Gravity

This paper presents a novel geometric interpretation of gauge field confinement within an algebraic framework unifying gravity and all Yang-Mills interactions. We demonstrate that gauge field flux tubes are fundamentally identical to torsion tubes in spacetime geometry. The theory is built upon an extended Clifford algebra structure with orthogonal imaginary units 𝑖, 𝑗, 𝑘, ℓ separating gauge sectors. The key result shows that the torsion 2-form 𝑇 𝑎 contains all gauge field strengths via 𝑇 𝑎 = Í𝛼 𝛽𝛼 𝑋𝛼 𝐹 ( 𝛼) ∧ 𝑒𝑎, establishing a direct geometric basis for gauge dynamics. We prove that Stokes’ theorem applied to torsion yields universal flux quantization conditions: ∮𝐶 Θ( 𝛼) = ∫𝑆 𝑋𝛼 𝐹 ( 𝛼) = 2𝜋𝑛𝛼 for all gauge groups. The model predicts confinement for non-Abelian groups with nontrivial centers (SU(3)𝑐), explains the absence of confinementfor broken symmetries (SU(2)𝐿 × U(1)𝑌 ), and naturally incorporates the Higgs mechanism and fermion masses. Specific predictions include string tensions, electroweak flux tubes, and testable modifications to particle physics phenomena.