Abstract
Within the mathematical framework of Quillen, one interprets the Higgs field as part of the superconnection 𝔻 on a superbundle. We propose to take as superbundle the exterior algebra ∧V obtained from a Hermitian vector bundle V of rank n with structure group U(n) and study the curvature F=D2. The Euclidean action, at most quadratic in 𝔽 and invariant under gauge transformations, depends on n+1 central charges. Spontaneous symmetry breaking is related to a nonvanishing constant scalar curvature in the ground state, F=Lc2, where Lc is the Higgs condensate. The U(1) Higgs model is nothing but the familiar Ginzburg–Landau theory, whereas the U(2) Higgs model relates to the electro-weak theory (without matter fields). The present formulation leads to the relation g2=3g′2 for the coupling constants, the formula sin2 θ=1/4 for the Weinberg mixing angle, and the ratio mW2:mZ2:mH2=3:4:12 for the masses of W±, Z0, and the Higgs boson. Experimentally observed deviations are attributed to loop corrections.
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