SO(10) Unification in Non-Commutative Geometry

Details SO(10) Unification in Non-Commutative Geometry SO(10) Unification in Non-Commutative Geometry

1993-04-07

arxiv.org/abs/hep-th/9304023v1

Phys.Rev. D50 (1994) 2893-2907

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, ZU-TH-10/1993 and ETH/TH/93/12

Scientific paper

10.1103/PhysRevD.50.2893

We construct an $SO(10)$ grand unified theory in the formulation of non-com-\break mutative geometry. The geometry of space-time is that of a product of a continuos four dimensional manifold times a discrete set of points. The properties of the fermionic sector fix almost uniquely the Higgs structure. The simplest model corresponds to the case where the discrete set consists of three points and the Higgs fields are ${\u {16}_s}\times \overline{\u {16}}_s$ and ${\u {16}_s}\times {\u {16}_s} $. The requirement that the scalar potential for all the Higgs fields not vanish imposes strong restrictions on the vacuum expectation values of the Higgs fields and thus the fermion masses. We show that it is possible to remove these constraints by extending the number of discrete points and adding a singlet fermion and a ${\u {16}_s}$ Higgs field. Both models are studied in detail.

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