Summary
D=7 theory on the squashed three-sphere with isometrySU(2)⊗U(1) is studied. The compact internal space is labelledA ts. The associated curvature is found to pass through zero and becomes increasingly negative. This offers a way to circumvent Lichnerowicz theorem. The geometrical couplings are computed and topologically related to the phenomenological ones withn g generation of fermions. Harmonic analysis of fermion fields onA ts space revealed that the only way to obain the right and lepton quantum numbers is to introduce an extraSU(2) group.
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Zerrouk, A.F. ElectroweakSU(2)⊗U(1) as a symmetry inD=7 space. Nuov Cim B 106, 579–592 (1991). https://doi.org/10.1007/BF02813226
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DOI: https://doi.org/10.1007/BF02813226