An electroweak theory of leptons in six dimensions

We present a theory of electroweak interactions in the lepton sector extended to six dimensions. This extension involves adding two additional time-like dimensions to the standard four-dimensional theory, resulting in a six-dimensional spacetime corresponding to the Clifford algebra C ℓ (3,3). A matrix representation of C ℓ (3,3) is used to construct Lorentz invariant quantities from its elements. We demonstrate that three specific elements of C ℓ (3,3) are sufficient to describe the eight lepton states of a single generation. Using these elements, we define a representation of SU(2)×U(1), leading to an electroweak theory that incorporates the chiral nature of the interactions. Our results show that components of the gauge bosons in the extra time-like dimensions form the graded superalgebra su ( 4 | 4 ) , which generates quadratic and quartic terms for the extra-dimensional components of the W bosons. These terms facilitate a vacuum expectation value and spontaneous symmetry breaking, providing a novel interpretation of the Higgs potential. We predict a tree-level Higgs mass from this potential to be half the vacuum expectation value, or m H = 123.11 GeV. Furthermore, the model predicts a Weinberg angle of θ W = 30 ∘ . This approach contrasts with previous models that utilized internal gauge symmetries and superalgebras like su ( 2 | 1 ) or su ( 2 | 2 ) , by deriving the superalgebra su ( 4 | 4 ) directly from the spacetime geometry of C ℓ (3,3).