Beyond the noncommutative standard model

[mitchell porter]

http://arxiv.org/abs/1304.8050
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...

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.

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

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.

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.

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

it became clear that the mass of the Brout-Englert-Higgs boson would not comply with the restriction (that m_H ≥ 170 Gev) imposed by the validity of the Standard Model up to the uni fication scale. This obstruction to lower m_H was overcome in [11] simply by taking into account a scalar fi eld which was already present in the full model

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.

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 which may be wrong, but which hasn't been shown to be wrong.

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 be the prediction 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 I am interested that I would like to see these problems cleared up.

 

[nicoo]

You may find some insights in here

http://arxiv.org/abs/0706.3688
Why the Standard Model
Ali H. Chamseddine, Alain Connes
(Submitted on 25 Jun 2007)
The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational explanation: space-time has a fine structure given as a product of a four dimensional continuum by a finite noncommutative geometry F. The raison d'etre for F is to correct the K-theoretic dimension from four to ten (modulo eight). We classify the irreducible finite noncommutative geometries of K-theoretic dimension six and show that the dimension (per generation) is a square of an integer k. Under an additional hypothesis of quaternion linearity, the geometry which reproduces the Standard Model is singled out (and one gets k=4)with the correct quantum numbers for all fields. The spectral action applied to the product MxF delivers the full Standard Model,with neutrino mixing, coupled to gravity, and makes predictions(the number of generations is still an input).

 

[humanino]

The Higgs mass prediction (updated) is at
Resilience of the Spectral Standard Model

We show that the inconsistency between the spectral Standard Model and the experimental value of the Higgs mass is resolved by the presence of a real scalar field strongly coupled to the Higgs field. This scalar field was already present in the spectral model and we wrongly neglected it in our previous computations. It was shown recently by several authors, independently of the spectral approach, that such a strongly coupled scalar field stabilizes the Standard Model up to unification scale in spite of the low value of the Higgs mass. In this letter we show that the noncommutative neutral singlet modifies substantially the RG analysis, invalidates our previous prediction of Higgs mass in the range 160--180 Gev, and restores the consistency of the noncommutative geometric model with the low Higgs mass.

None of the statements are vague, everything has a precise, well-defined, mathematical meaning in those papers. I agree that the Higgs mass post-diction is most unfortunate.

 

[arivero]

Which Higgs is the composite? Is the Pati-Salam breaking higgs a composite of the electro-weak breaking higgs, or is it in the reversal direction?

It could be of some relevance for theories of extra dimensions because Pati-Salam is living just out-of-bounds there, in D=12, while the SM gauge symmetry unbroken lives in D=11. (The NCG models happen to live in 10 mod 8, but they are formulated with Euclidean metrics, not Riemannian, so a direct comparison is tricky). Remember that max SUGRA, as well as M-theory, lives in D=11.

The point is that while it could be reasonable to use compatification to break first from Pati-Salam to SM (D=12 to D=11) and then from SM to SU(3)xU(1) (so D=9), the compactification mechanism can (and should?) be different, because in the first case it does not need to be based in SUGRA, and in the second case we want to be able to use SUGRA, or even M-Theory, as we are in its ballpark.

Note that the SM as Nature tell us is not fully unbroken (D=11) nor fully broken (D=9) but something in the middle. Note also that in D=11 we can not produce the charges nor the chiralities of the SM. It has been argued that the at least the former problem is solved in D=12.

 

[mitchell porter]

In search of enlightenment regarding the nature of the NC standard model, especially its relation to more familiar formalisms, I went back to the blog discussions of 2008.

One issue was, how is it that the NC standard model makes predictions for quantities that are necessarily free parameters in the "QFT standard model"? Motl took the position that such predictions must be illusions - if a new formalism equivalent to QFT, it must allow all the couplings to take any value, even if its inventors don't currently see how to do that.

Then he says that it might also be viewed as a truncation of a stringy vacuum, with the massive higher-dimensional states discarded. Here he is inviting Connes to learn string theory and apply his insights to it.

But one of the features of string theory is that you can't have just any QFT with any values of the couplings, as the field-theory limit. So could it be that some of the extra constraints of the NC standard model are real after all, and have a similar origin?

Distler has much more to say about the technicalities of the NC standard model. For him, below the scale Λ, it's just an effective field theory, and above the scale Λ, it's defined only as an underspecified classical theory that we don't know how to quantize. The peculiar constraints on the constants of the EFT all seem to come from the way things are defined at this higher scale.

Finally, [URL='https://www.physicsforums.com/insights/author/urs-schreiber/']Urs Schreiber[/URL] speculates in some detail about how the NC standard model might be embedded in string theory. He suggests that it corresponds to a "non-geometric phase" of string theory, i.e. a vacuum where there aren't extra spatial dimensions, just extra degrees of freedom on the strings that lack a geometric interpretation. His position implies that the NC standard model wasn't singled out by pure reason alone, but that the principles used to zero in on it were empirical, i.e. Connes et al are building phenomenological models.

As for Pati-Salam showing up now... The procedure that singles out the NC standard model for attention arrives at a particular algebra, then focuses on a particular subalgebra as suitable for the intended construction. Pati-Salam is supposed to arise by looking back at the larger algebra and relaxing one of the conditions of the construction. But from a stringy point of view... I was sure I read somewhere recently, of work by Kieth Dienes suggesting that the Pati-Salam group is generic in the landscape. I can't now find the reference or any such paper by Dienes. But it would be interesting if something like Schreiber's interpretation of NCG physics is correct - that these are non-geometric phases of string theory - and if the appearance of a Pati-Salam symmetry one level up from the NC standard model, had something to do with Pati-Salam being the usual path to the standard model in the string landscape.

 

[ohwilleke]

I have to share skepticism regarding the "uniquely" part. The group theory constraints may get you to a full set of fermions and bosons, but I don't see how it fixes any of the dozens of SM constants. And, a four color model (presumable with three quark colors and one lepton color that for some reason doesn't fit with the quark color - one is tempted to look to quark color as a polarization in three spatial dimensions and lepton character as a polarization in a time-like dimension) with one color that isn't really like the others is hardly natural.

It also is not at all obvious that this unification solves all the problems that sunk early Pati-Salam unification efforts (proton decay, flavor changing neutral currents, magnetic monopoles, etc.) in a convincing way.

 

[humanino]

Fixing the group structure has nothing to do with fixing the coupling constants. The SM constants still have to be measured. This is old and has been discussed numerous times in many places. If you are interested, you should seriously read before criticizing.

 

[arivero]

Well, the "uniqueness" is only about higgs and gauge, not about fermions. Gauge uniqueness is not surprising, the new thing in Connes that gauge implies Higgs, or if you prefer, that the Algebra implies both.

It is remarkable that the research on NCG is accelerating. It has only taken seven years to get a new idea, this time. Last gap was about ten years.

 

[arivero]

Now, I like the idea of a composite structure for the A(2) in terms of A(1) because it paves the way to think of A(1) as a composite in terms of D, which is to say, in terms of the fermion structure.

 

[mitchell porter]

I like the idea of a composite structure for the A(2) in terms of A(1) because it paves the way to think of A(1) as a composite in terms of D, which is to say, in terms of the fermion structure.

..

The resulting model is very similar to the one considered by Marshak and Mohapatra

..

We consider the "minimal" model, namely only those kinds of Higgs multiplets that can arise as bound states of existing fermion multiplets.

 

[arivero]

It is sort of amusing that we also call Pati-Salam also to the ideas of Mohapatra and Senjanovic.

As for the compositeness, the preprint "Composite Weak Bosons and Origin of Fermi Coupling Constant", of Mohapatra (1982), is available in KEK, according http://inspirehep.net/record/178059?ln=es. The abstract tells that also the Majoron is a composite in this kind of models.

 

[ohwilleke]

Fixing the group structure has nothing to do with fixing the coupling constants. The SM constants still have to be measured. This is old and has been discussed numerous times in many places. If you are interested, you should seriously read before criticizing.

FWIW, the group structure of the model proposed doesn't even actually reproduce the SM. It adds in RH neutrinos, for example.

 

[mitchell porter]

I was sure I read somewhere recently, of work by Keith Dienes suggesting that the Pati-Salam group is generic in the landscape

The claim is made in hep-th/0602286 (page 28); and I read about it in arxiv:1304.6092 ... which is of independent interest in this discussion, because it is about getting Pati-Salam from a different approach to noncommutative physics.

More precisely, I have learned through Alejandro that in the 1990s there was an alternative approach to the noncommutative SM, the "Marseilles-Mainz model", which instead of starting with a Dirac operator and then obtaining the gauge fields, started with the bosons and then built on them a superconnection containing fermionic degrees of freedom. ("Connes-Lott" and "Marseilles-Mainz" are compared in http://repositories.lib.utexas.edu/bitstream/handle/2152/1872/asakawat042.pdf?sequence=2.) This work employed the supergroup su(2|1), and the second paper above obtains left-right symmetry (as in Pati-Salam) from su(2|2).

edit: OK, I notice that the paper from last month is not really about noncommutative physics. Instead, they suggest that the su(2|1) electroweak model had similar problems to the NC standard model of Connes et al, and can similarly be fixed by an extra scalar, which is obtained by going to su(2|2).

 

[arivero]

T
More precisely, I have learned through Alejandro that in the 1990s there was an alternative approach to the noncommutative SM, the "Marseilles-Mainz model", .

A track of the first ten years of NCG models is here

http://dftuz.unizar.es/~rivero/research/ncactors.html

The Red Book is available in pdf in the website of Alain Connes, http://www.alainconnes.org/en/

 

[arivero]

It could be just my poor grasp of English grammar, but this phrase puzzles me:

http://arxiv.org/abs/1304.8050][/PLAIN]
The Higgs fields are composite, the fundamental ones being of similar
form to those formed from the fermion bilinears.