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arivero
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I got some spare time to glance at "[URL
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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
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)).
[/URL]
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
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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