A topological model of composite preons from the minimal ideals of two Clifford algebras

Abstract

This paper demonstrates a direct correspondence between a recent algebraic characterization of leptons and quarks as basis elements of the minimal one-sided ideals of the complex Clifford algebras Cℓ(6) and Cℓ(4), shown earlier to transform as a single generation of leptons and quarks under the Standard Model's unbroken SU(3)c×U(1)em and SU(2)L gauge symmetries respectively, and a topological formulation of the Harari-Shupe preon model in which leptons and quarks are represented in terms of braids.It was previously shown that mapping a Witt basis of Cℓ(6) to particular braids in the circular Artin braid group B3c makes it possible to replicate the topological structure describing electrocolor symmetries in this preon model. This paper extends this curious correspondence, which involves only the minimal ideals of Cℓ(6) under SU(3)c×U(1)em, to include the SU(2)L chiral weak symmetry. This is achieved by mapping a Witt basis of an additional Cℓ(4) algebra to braids in B3, taken to be a subgroup of B3c. The braids corresponding to the charged vector bosons are determined, and it is demonstrated that chiral weak interactions can be described via the composition of braids.