Non-commutative Complex Projective Spaces and the Standard Model

Details Non-commutative Complex Projective Spaces and the Standard Model Non-commutative Complex Projective Spaces and the Standard Model

2003-07-14

arxiv.org/abs/hep-th/0307124v1

Mod.Phys.Lett. A18 (2003) 2319-2328

Physics

High Energy Physics

High Energy Physics - Theory

Contribution to conference in honour of A.P. Balachandran's 65th birthday: "Space-time and Fundamental Interactions: Quantum A

Scientific paper

10.1142/S0217732303012532

The standard model fermion spectrum, including a right handed neutrino, can be obtained as a zero-mode of the Dirac operator on a space which is the product of complex projective spaces of complex dimension two and three. The construction requires the introduction of topologically non-trivial background gauge fields. By borrowing from ideas in Connes' non-commutative geometry and making the complex spaces `fuzzy' a matrix approximation to the fuzzy space allows for three generations to emerge. The generations are associated with three copies of space-time. Higgs' fields and Yukawa couplings can be accommodated in the usual way.

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