Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
The assumption that space-time is a noncommutative space formed as a product of a continuous four dimensional manifold times a finite space predicts, almost uniquely, the Standard Model with all its fermions, gauge fields, Higgs field and their representations. A strong restriction on the noncommutative space results from the first order condition which came from the requirement that the Dirac operator is a differential operator of order one. Without this restriction, invariance under inner automorphisms requires the inner fluctuations of the Dirac operator to contain a quadratic piece expressed in terms of the linear part. We apply the classification of product noncommutative spaces without the first order condition and show that this leads immediately to a Pati-Salam SU(2)_{R} x SU(2)_{L} x SU(4) type model which unifies leptons and quarks in four colors. Besides the gauge fields, there are 16 fermions in the (2,2,4) representation, fundamental Higgs fields in the (2,2,1), (2,1,4) and (1,1,1+15) representations. Interestingly we encounter a new phenomena where the Higgs fields in the high energy sector are composite and depend quadratically on the fundamental Higgs fields. The Pati-Salam symmetries are broken spontaneously at high energies to those of the Standard Model.
View original:
http://arxiv.org/abs/1304.8050
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