# New Connes: Gravity and the standard model with neutrino mixing

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## Main Question or Discussion Point

I put a notice of this earlier today in the QG links thread
https://www.physicsforums.com/showpost.php?p=1134904&postcount=529

This thread is in case anyone wishes to discuss the paper:

http://arxiv.org/abs/hep-th/0610241
Gravity and the standard model with neutrino mixing
Ali H. Chamseddine, Alain Connes, Matilde Marcolli
71 pages, 7 figures

"We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector."

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Summary paragraph from page 5:

===quote===
In summary we have shown that the intricate Lagrangian of the standard model coupled with gravity can be obtained from a very simple modification of space-time geometry provided one uses the formalism of noncommutative geometry. The model contains several predictions and
the corresponding section 5 of the paper can be read directly, skipping the previous sections. The detailed comparison in section 4 of the spectral action with the standard model contains several steps that are familiar to high energy particle physicists but less to mathematicians. Sections 2 and 3 are more mathematical but for instance the relation between classical moduli spaces and the CKM matrices can be of interest to both physicists and mathematicians. The results of this paper are a development of the preliminary announcement of [17].
===endquote===

Kea
Oooh, goody.

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Kea said:
Oooh, goody.
You are the one who can tell us what this new paper does that goes beyond the one Connes posted a couple of months ago (at the same time that Barrett posted his)

The August paper
http://arxiv.org/abs/hep-th/0608226
was titled
"Noncommutative Geometry and the standard model with neutrino mixing"
and I get the impression (although I am quite unsure about this) that the 17-page August paper contained all the research results----which he was in a hurry to get out there in a timely fashion.

And that the October paper which is 71-pages and done with his two usual collaborators is essentially just providing all the details.

But actually I am finding the first few pages of the long paper CLEARER for some reason. Maybe he takes more time with the exposition. Do you also find it more helpful? I can't say I understand it but I come closer to with the introduction section of this second paper.

Anyway, any explaining you want to do would be appreciated

arivero
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marcus said:
Ke
But actually I am finding the first few pages of the long paper CLEARER for some reason.
The collaborators probably are of some help here.

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John Baez already showed that there is a Calabi-Yau manifold whose holonomy group is the reduced gauge group of the standard model. This should have put us on notice that the SM with all its peculiar interacting quiddities could be modeled geometrically without however explaining any of the quiiddities.

So Connes et al. have found a manifold that does this in impressive detail. Verrrry interesting, but as I said we should have expected someone to find one. And then they cross this fancy-schmanzy manifold with Einstein spacetime and say "Voila! Gravity and the SM in one model!" See what I mean?

Kea am I way off base here?

Kea
And then they cross this fancy-schmanzy manifold with Einstein spacetime and say "Voila! Gravity and the SM in one model!"

There must be other people out there who know more about this than me. Anyway I've only glanced at it so far, and it looked just like a 70+ page version of the short paper to me. Remember that Connes never claimed to have any idea at all about the QG angle on this. He said so in his talk. And they quite clearly put the number of generations in by hand. I really don't see, therefore, that the predictions amount to much, even if the Lagrangian is right, because it can't do QG. However, we don't have another rigorous QFT quite yet, so this is certainly significant. Any improvement should be capable of reproducing the NCG language.

On a slightly different note (nothing to do with the SM): I actually went to a very interesting NCG talk today by Paolo Bertozzini (maybe I'll blog about it) which made a couple of things a little bit clearer to me. Paolo works on a kind of categorification of the basic (spectral triple / manifold) duality, and thinks of this Tomita-Takesaki stuff that they're keen on (http://arxiv.org/abs/math-ph/0511034) as providing a C* version of the Cosmic Galois Group somehow. But he ends up doing bundles instead of manifolds and then he says they might be like gerbes or stacks ... and he wants to put it all into a more categorical language.

Cheers

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arivero
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Kea said:
. And they quite clearly put the number of generations in by hand.
Note 2.7, about the CKM and MNS (now PNMS?) matrices. My guess is that they hope to find some hint from CP violation; remember that CP violation forces n>2. If they can find a clear geometrical meaning of CP violation, then they have got a way to explain the number of generations.

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Kea said:
On a slightly different note (nothing to do with the SM): I actually went to a very interesting NCG talk today by Paolo Bertozzini (maybe I'll blog about it) which made a couple of things a little bit clearer to me. Paolo works on a kind of categorification of the basic (spectral triple / manifold) duality, and thinks of this Tomita-Takesaki stuff that they're keen on (http://arxiv.org/abs/math-ph/0511034) as providing a C* version of the Cosmic Galois Group somehow. But he ends up doing bundles instead of manifolds and then he says they might be like gerbes or stacks ... and he wants to put it all into a more categorical language.
I'm going to take this and start a new thread on AQFT approaches to QG. Bert Shroer linked to a paper in a recent comment on Woit's post about his (Shroer's) Samizdat which i'll include too. This work seems very promising to me. Let a hundred flowers bloom!

Kea
arivero said:
If they can find a clear geometrical meaning of CP violation...
Hi arivero

Glad to see that you might actually read this! Finding a geometrical description of CP violation doesn't explain it.

arivero
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Kea said:
Hi arivero

Glad to see that you might actually read this! Finding a geometrical description of CP violation doesn't explain it.

I used an intentional wording: "a way to explain", ambiguosly meaning "a path towards explaining"

arivero
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arivero said:
I used an intentional wording: "a way to explain", ambiguosly meaning "a path towards explaining"
said that, I have been speculating on other posible ways. This 8-periodicity rings like the one of unimodular selfdual lattices, and I have been tempted to think that with one generation you have an algebra related to the E8 lattice, with three you get the Leech lattice.

On the other hand, the oldest approach had a way to ask for more than one generation because the mass matrix was asked to be non degenerated: the Higgs field was related to the ortogonal projection of the generation masses (yukawa couplings, if you wish) against the vector (1,1,1). A pity it was about generation masses, and not their square root . But I wonder what happens if the new algebra is used to work out the old method. In principle both models were equivalents, but now the new one has a peculiar dirac operator, with majonana masses.

arivero
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An extra comment: the most meat of this paper, as in the last one, goes to the appendix. The appendixes seem intended to avoid you to refer to prior work, but actually they are more of a refreshment.

One refreshing new item is the important inclusion of the neutrino.

Bahcall equations from 'Solving the Mystery of the Missing Neutrinos' by John N Bahcall in 2004 - appear to suggest that the Earth rotates and orbits in a sea [ether?] of neutrinos:
"... About 100 billion neutrinos from the Sun pass through your thumbnail every second, but you do not feel them because they interact so rarely and so weakly with matter. Neutrinos are practically indestructible; almost nothing happens to them. For every hundred billion solar neutrinos that pass through the Earth, only about one interacts at all with the stuff of which the Earth is made ..."
http://nobelprize.org/nobel_prizes/physics/articles/bahcall/

Do neutrinos replenish the geomagnetic core?

a - electrons are probably created from interaction with magma around an iron core [does this produce electromagnetism with a supply of neutrinos that may last for another 5 billion years?]
b - Cherenkov radiation should produce light, but may produce heat in the core

Do a and b account for the absence of about 50% of the neutrinos from the antipodal sun side?

arivero
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Ah, if you are about Cambridge, the seminars on this paper will follow during this week and the next one, plus a generic talk, more concentrated, somewhere in the middle. Check the newton institute webpages.

John Baez already showed that there is a Calabi-Yau manifold whose holonomy group is the reduced gauge group of the standard model. This should have put us on notice that the SM with all its peculiar interacting quiddities could be modeled geometrically without however explaining any of the quiiddities.
Why on earth should the holonomy group (of a manifold) coincide with the SM gauge group? Morally it is the complement of the gauge group in a larger group, and the larger the holonomy group becomes (ie the more curved the manifold is), the less symmetries will be preserved and the smaller the gauge group becomes...

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John Baez already showed that there is a Calabi-Yau manifold whose holonomy group is the reduced gauge group of the standard model. This should have put us on notice that the SM with all its peculiar interacting quiddities could be modeled geometrically without however explaining any of the quiiddities.
...
I remember seeing that paper.

http://arxiv.org/abs/hep-th/0511086
Calabi-Yau Manifolds and the Standard Model
John C. Baez
4 pages

"For any subgroup G of O(n), define a "G-manifold" to be an n-dimensional Riemannian manifold whose holonomy group is contained in G. Then a G-manifold where G is the Standard Model gauge group is precisely a Calabi-Yau manifold of 10 real dimensions whose tangent spaces split into orthogonal 4- and 6-dimensional subspaces, each preserved by the complex structure and parallel transport. In particular, the product of Calabi-Yau manifolds of dimensions 4 and 6 gives such a G-manifold. Moreover, any such G-manifold is naturally a spin manifold, and Dirac spinors on this manifold transform in the representation of G corresponding to one generation of Standard Model fermions and their antiparticles."

Although discussion of this paper properly belongs in Biophysics, recall that peptides are arranged in angles that might conform to yaw, pitch and roll that may be related to Connes NCG.

Now the number 1.61 appears in electrostatic genome packing.
Could it be that electromagnetism is inherent in peptides and nucleic acids [loops and strings]?

http://www.pnas.org/cgi/content/abstract/0608311103v1
Published online before print November 7, 2006
Proc. Natl. Acad. Sci. USA, 10.1073/pnas.0608311103
Physics
Biophysics
Electrostatic origin of the genome packing in viruses
( polymer assembly | capsid structure )
Vladimir A. Belyi and M. Muthukumar *
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003
Communicated by Richard S. Stein, University of Massachusetts, Amherst, MA, September 26, 2006 (received for review February 15, 2006)
Abstract:
Many ssRNA/ssDNA viruses bind their genome by highly basic semiflexible peptide arms of capsid proteins. Here, we show that nonspecific electrostatic interactions control both the length of the genome and genome conformations. Analysis of available experimental data shows that the genome length is linear in the net charge on the capsid peptide arms, irrespective of the actual amino acid sequence, with a proportionality coefficient of 1.61 ± 0.03. This ratio is conserved across all ssRNA/ssDNA viruses with highly basic peptide arms, and is different from the one-to-one charge balance expected of specific binding. Genomic nucleotides are predicted to occupy a radially symmetric spherical shell detached from the viral capsid, in agreement with experimental data.
Author contributions: V.A.B. and M.M. performed research and wrote the paper.
The authors declare no conflict of interest.
*To whom correspondence should be addressed.
M. Muthukumar, E-mail: muthu@polysci.umass.edu
www.pnas.org/cgi/doi/10.1073/pnas.0608311103

Calabi-Yau Manifolds and the Standard Model [John C. Baez]

Hi Marcus:

As I interpret the paper referenced in your comment of 11-06-2006 01:10 PM, both
a - Proposition 1 and
b - Corollary 1
appear to reconcile a 10D Calabi-Yau manifold decomposed into 4D and 6D manifolds that are equivalent to complex-2D and complex-3D twistor [not tensor] [Penrose] manifolds.

If I interpret this correctly, then twistor string theory [Witten] may be equivalent to one or all of the five recognized string theories within M-theory.

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Kea
Dcase said:
If I interpret this correctly, then twistor string theory [Witten] may be equivalent to one or all of the five recognized string theories within M-theory.
Shhhhh, Dcase!

arivero
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The more I look the more I am worried about the scale to be applied to Connes new model. There is the prediction
$$y_e^2+y_\nu^2+3y_u^2 +3y_d^2 = 4 g^2$$

or
$$m_e^2+m_\nu^2+3m_u^2 +3m_d^2 = 8 M_W^2$$
that Connes aplies at GUT scale considering that the yukawa coupling of the neutrino is also near unity. In this case the renormalization group saves the day giving a yukawa coupling of 1.14 for the top quark, not far but more than 10% off mark.

But on the other hand the equation, with the approximation of the 3rd neutrino yukawa equal to the top one, and all the others negligible, can be taken to say that

$$4 y_t^2 = 4 g^2$$

And on the other hand remember $$g_s^2=g^2=\frac 53 g_1^2$$

Well I know that $$y_t$$ is equal 1 at low energy. And I know that $$g_s=1$$ at low energy. So there is two votes for considering the model in the infrared instead of the ultraviolet. Of course the votes against come from the electroweak couplings. Neither the weak isospin coupling is equal one nor the hypercharge is nearby 0.77...

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