SO(10) Unification in Non-Commutative Geometry

Abstract

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 ${\breve{16}}_s\times {\overline{\breve{16}}}_s$ and ${\breve{16}}_s\times {\breve{16}}_s$. 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 ${\breve{16}}_s$ Higgs field. Both models are studied in detail.

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

References in corpus (5)

• Gravity in Non-Commutative Geometry
• Grand Unification in Non-Commutative Geometry
• Parameter restrictions in a non-commutative geometry model do not survive standard quantum corrections
• Higgs Mass and Noncommutative Geometry
• Constraints on the Higss and Top Quark Masses From Effective Potential and Non-Commutative Geometry

Cited by in corpus (13)

• Connes' Model Building Kit
• Differential Algebras in Non-Commutative Geometry
• Noncommutative Kaluza-Klein Theory
• Beyond the standard model with six-dimensional spinors
• A Left-Right Symmetric Model a la Connes-Lott
• Fuzzy Mass Relations for the Higgs
• Thermodynamics on Fuzzy Spacetime
• GUTs without guts
• BRST invariant Lagrangian of spontaneously broken gauge theories in noncommutative geometry
• The Scalar Potential in Noncommutative Geometry
• A Partial Unification Model in Non-commutative Geometry
• A Tour through Non-Associative Geometry
• SU(5) orbifold GUT in noncommutative geometry