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This is a separate thread to discuss another idea by arivero, originally https://www.physicsforums.com/showthread.php?t=485247&page=4#63".Some references: arivero said: ↑After all this LHC excitation, I am afraid i could go into hibernation for some period, but I want to say some words about this 313 GeV thing and how, to my regret, it could relate to extra dimensions. The point is that if we want quarks and leptons to stand in some symmetry group, the smaller candidate is SU(4), "Lepton number as the fourth color". The full group Pati Salam thing, SU(4)xSU(2)xS(2), is known to appear with 8 extra dimensions: it is the group of isometries of the manifold S5xS3, the product of the three-sphere with the five-sphere. It was argued by Bailin and Love that 8 extra dimensions are needed to get the charge assignmens of the standard model, but I am not sure if this manifold was used. Its role was stressed by Witten, who pointed out that the family of 7-dimensional manifolds that you get by quotienting this one via an U(1) action have the isometry group SU(3)xSU(2)xU(1).

I liked to think of this compactification as an infinitesimal extra dimension, partly because of the hint of F-theory, partly because thile the SU(4) group seems a need, I don't like to look at it as alocalgauge group.

Again, this was well known lore of supergravity (and even in string theory) in the early eighties, but in the same way that the first revolution wiped gluons away, the second string revolution killed the research on realistic Kaluza Klein theories.

http://www.sciencedirect.com/science/article/pii/0550321385902329" [Broken])

http://iopscience.iop.org/0034-4885/50/9/001". D Bailin and A Love, 1987. Rep. Prog. Phys. 50 1087.

The second article is a review of Kaluza-Klein theories and is noteworthy for going over the crucial arguments, due to Witten, about the difficulties of obtaining chiral fermions in KK theories, even if one adds torsion. Some of those arguments are from Witten's paper "Fermion Quantum Numbers in Kaluza-Klein Theory", which is apparently only available in the proceedings of the "Shelter Island II" conference from 1983.

It's curious that the first paper, on KK theories in 12 dimensions, is apparently completely uncited in the literature on F-theory, which suggests either that there's an obvious reason why one can't interpret F-theory in this way, or that the old KK lore really was forgotten.

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# Kaluza-Klein theories in twelve dimensions and F-theory

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