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Section 9.2 is awesome. It tells us that the discrete algebras of NCG should be interpreted as a low energy residual of a NC deformation of an extra dimensional manifold. For instance, a single M_4(C) is a hint of a deformation of the sphere S4.

Basically, Connes and Chamseddine are reporting now a mathematical three-sigma experimental evidence for kaluza klein theory.

1-sigma: red book NCG, Connes-Lott see http://dftuz.unizar.es/~rivero/research/ncactors.html [Broken]

2-sigma: 6 dimensional spectral triple, Connes-Chamseddine-Marcolli 2006

3-sigma: Connes-Chamseddine 2010

4-sigma: production of the manifold related to M_2(H)+M_4(C).

5-sigma: ?

Let me note that it could be a six dimensional manifold related to a 8 dimensional one, or reciprocally, because we know that:

- Pati Salam needs 8 extra dimensions (same than other L-R models, btw).

- Standard Model unbroken needs 7 extra dimensions.

- a lot of people needs 6 extra dimensions.

- SU(3)xU(1) EM (the unbroken group of the SM) can live in 5 extra dimensions (same than pure SU(4), btw, because su(4)=so(6)).

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# Chamseddine Connes

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