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Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification

Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom

(Submitted on 30 Apr 2013)

I have a few questions about this paper...

How good is "almost uniquely"? i.e. it would be good to see this argument spelled out. 1304.8050 said: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.

So the claim is that assuming noncommutative geometry "almost uniquely" predicts the standard model. Then, if we remove a "first order condition" - which is perhaps one of the necessary extra assumptions that puts the "almost" in "almost uniquely" - then "this leads immediately" to a Pati-Salam model. 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.

Those quotes are from the abstract. Then, a short distance into the paper...

But Estrada and Marcolli wrote a paper which was Standard Model up to the Planck scale, and they managed to get 125 GeV the same way Shaposhnikov and Wetterich did, i.e. by assuming asymptotic safety of gravity, which forces a number of couplings to go to zero at the Planck scale. it became clear that the mass of the Brout-Englert-Higgs boson would not comply with the restriction (thatm≥ 170 Gev) imposed by the validity of the Standard Model up to the unification scale. This obstruction to lower_{H}mwas overcome in [11] simply by taking into account a scalar field which was already present in the full model_{H}

So I have two issues.

First, I am skeptical about the claims that the standard model - and now, this Pati-Salam model - are unique or inevitable consequences of doing physics via noncommutative geometry. Presumably there are some true technical statements which lie behind these bold but vague claims; it would be good to know what they are.

Second, I am confused about the claim that the noncommutative standard model predicted that the Higgs mass had to be at least 170 GeV. Asymptotic safety is a hypothesis that may or may not be true - Estrada and Marcolli's calculation is based on assuming that it's a property of the model ... but I don't understand how the noncommutative standard model can be said unequivocally to make a certain prediction, when a completely different prediction is implied, by the use of an ansatz for the same model, an ansatz whichmaybe wrong, but which hasn't beenshown to bewrong.

What I'm saying: if there's room for doubt about the high-energy behavior of the model, and if the different possibilities lead to dramatically different low-energy predictions, then how can just one of those predictions be said to betheprediction made by the model?

Let me add that I'm asking these questions because I think that noncommutative geometry really may have something to tell us about reality! If these were just incomprehensible crackpot papers where the author first finds that "inevitably" their theory matches the data, and then when the data changes, they study their incomprehensible model further and discover that it "inevitably" matches the new data... I wouldn't be interested. It's because Iaminterested that I would like to see these problems cleared up.

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# Beyond the noncommutative standard model

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