Baez links Standard Model symmetries to Calabi-Yaus

[marcus]

new preprint
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..."

quote:"It would be nice to find a use for these results."

------------------
Just in case some might be interested I will mention another preprint posted today:

http://arxiv.org/physics/0511067
The Universe is a Strange Place
Authors: Frank Wilczek
Public lecture delivered at Lepton-Photon 2005, Uppsala, Sweden, and in related forms on several other occasions. To be published in the Proceedings. 14 pages, 6 figures

"Our understanding of ordinary matter is remarkably accurate and complete, but it is based on principles that are very strange and unfamiliar. As I'll explain, we've come to understand matter to be a Music of the Void, in a remarkably literal sense. Just as we physicists finalized that wonderful understanding, towards the end of the twentieth century, astronomers gave us back our humility, by informing us that ordinary matter -- what we, and chemists and biologists, and astronomers themselves, have been studying all these centuries constitutes only about 5% of the mass of the universe as a whole. I'll describe some of our promising attempts to rise to this challenge by improving, rather than merely complicating, our description of the world."

Wilczek has used this title before. It is an evolving popular lecture---maybe it gets better or at least different, each time.

-------------------

this was posted a couple of days ago:

http://arxiv.org/abs/gr-qc/0511026
Gravitational solution to the Pioneer 10/11 anomaly
J. R. Brownstein, J. W. Moffat
11 pages, 4 figures, 1 table
"A fully relativistic modified gravitational theory including a fifth force skew symmetric field is fitted to the Pioneer 10/11 anomalous acceleration. The theory allows for a variation with distance scales of the gravitational constant G, the fifth force skew symmetric field coupling strength omega and the mass of the skew symmetric field mu=1/lambda. A fit to the available anomalous acceleration data for the Pioneer 10/11 spacecraft is obtained for a phenomenological representation of the "running" constants and values of the associated parameters are shown to exist that are consistent with fifth force experimental bounds. The fit to the acceleration data is consistent with all current satellite, laser ranging and observations for the inner planets."

 

[selfAdjoint]

Astounding. Obviously deep, even if mysterious. He references Zee, Chapter VII. I believe this is chapter VII.7 (7^2?) titled SO(10) Unification. I am going to study it.

This may explain, though why so many string models produce "near miss" versions of the standard model.

 

[Chronos]

I too was intrigued by the Brownstein paper. It looks like a well reasoned approach that does not tip any cows. The Wilczek paper is just another in his trademarked series of 'must read' papers. I can't intelligiently comment on Baez's paper. I'm still at the barely can spell Calabi-Yau manifold stage.

 

[selfAdjoint]

I thought it might be a good idea to provide a quick link to the Mathworld's definition of holonomy group, since that concept plays an important role in the new John Baez paper. Here it is: http://mathworld.wolfram.com/HolonomyGroup.html

Also Peter Woit has commented on the paper and in the comments Lubos exhibits "SST Blinkers" by asserting that since the holonomy symmetry is broken in string math it cannot be meaningful in any context.

 

[Kea]

It would be nice to find a use for these results.

Wow! And the String theorists never figured this out? I don't think I've ever been more astonished.

Kea

 

[marcus]

... Peter Woit has commented on the paper and in the comments Lubos exhibits "SST Blinkers" by asserting that since the holonomy symmetry is broken in string math it cannot be meaningful in any context.

Also CarlB recently started a thread about this Baez paper in "particles" forum
https://www.physicsforums.com/showthread.php?p=829362#post829362

anyone who hasnt already checked it out might be interested in doing so
among those posting were hans dV , arivero, arkhron

the discussion at Peter Woits went on for over 60 comments
http://www.math.columbia.edu/~woit/wordpress/?p=291

 

[josh1]

Hi selfAdjoint,

Lubos exhibits "SST Blinkers" by asserting that since the holonomy symmetry is broken in string math it cannot be meaningful in any context.

Would you mind explaining what the conventional way of thinking about the physical role of holonomy in calabi-yau spaces is and it`s relation to the standard model as Baez presents it? In particular, could you say something about the significance of symmetry breaking in this? I'm just not entirely sure that your inference about what lubos said is correct.

 

[selfAdjoint]

Hi selfAdjoint,


Would you mind explaining what the conventional way of thinking about the physical role of holonomy in calabi-yau spaces is and it`s relation to the standard model as Baez presents it? In particular, could you say something about the significance of symmetry breaking in this? I'm just not entirely sure that your inference about what lubos said is correct.

Here is Lubos Motl's quote from the comments on Peter Woit's Not Even Wrong discussion of John Baez's paper:

wants to study, for a very incomprehensible reason, manifolds whose holonomy coincides with the Standard Model gauge group

The last point seems completely crazy because holonomy is exactly the symmetry - a part of the tangential group - that is broken by the manifold’s shape, while the gauge group of the Standard Model is a group that must be, on the contrary, completely unbroken

In the context of string theory the breakng of the symmetry is a breaking of spacetime symmetry since the Calabi-Yau manifolds there are precisely carriers of the spatial dimensions beyond three. But in Baez's discovery, there is no such implication. He specifically does NOT state just what role his manifold does or should play in the standard model. Therefore there is no obvious link from the symmetry breaking to the requirements of the standard model. My statement about Lubos' blinders was to call attention to his unexamined assumptions about the Calabi-Yau's role in physics versus what Baez presented.

 

[Juan R.]

the discussion at Peter Woits went on for over 60 comments
http://www.math.columbia.edu/~woit/wordpress/?p=291

Discussion of Baez 'article' in Woit page is interesting.

I find just curious that nobody replied to my question

What is your opinion on

the relationship between Cosmology and quantum electrodynamics claimed on Hoyle F. and Narlikar, J. V. Reviews of modern Physics 1995, 67(1) 113-155?

Juan R.

Center for CANONICAL |SCIENCE)

on Woit blog.

Some related comments on Baez paper and why one would first work in a solid Standard Model for ALL phenomena (not only scattering epxerimetns on acellerator physics) see

http://canonicalscience.blogspot.com/2005/11/post-about-standard-model-on-peter_10.html

It is interesting as many physicists ignore recent experimental data (Radiation Physics and Chemistry. 2004, 71, 611–617):

The highly accurate measurements of hydrogen and helium, mentioned above, are also in strong disagreement with current QED theory.

 

[selfAdjoint]

It is interesting as many physicists ignore recent experimental data (Radiation Physics and Chemistry. 2004, 71, 611–617):


Quote:
The highly accurate measurements of hydrogen and helium, mentioned above, are also in strong disagreement with current QED theory.

Quoting your own website isn't providing evidence. Do you have any substantive links to support this claim?

 

[marcus]

Here is Lubos Motl's quote from the comments on Peter Woit's Not Even Wrong discussion of John Baez's paper:
"wants to study, for a very incomprehensible reason, manifolds whose holonomy coincides with the Standard Model gauge group
The last point seems completely crazy because holonomy is exactly the symmetry - a part of the tangential group - that is broken by the manifold’s shape, while the gauge group of the Standard Model is a group that must be, on the contrary, completely unbroken"

Lubos does not use the term "completely crazy". He uses the term "rather unnatural". If peter woit has indeed misrepresented lubos by replacing the term “rather unnatural” with “completely crazy”, I’m sure you’ll want to alert him straight away.
Now let's see if “rather unnatural” is appropriate.
...

Josh1 you raise the possibility that Lubos' post was typed by Lubos to say some words ("rather unnat.") WHICH THEN PETER WOIT CHANGED against Lubos intent to some other words ("compl. crazy"). Which is how it reads. Also without giving readers any notice that he had edited. And, if Lubos objected to having his comment tinkered, as one might expect, suppressing Lubos objection. That is a serious slur on Woit's integrity---a blogger shouldn't tinker with his guest's comments unless he's merely editing out obscenity, even in which case he should at least mark the post as edited.
Just for reference I went and copy-pasted from the orig. source:
http://www.math.columbia.edu/~woit/wordpress/?p=291#comments

Luboš Motl Says:
November 8th, 2005 at 10:32 pm
As far as I understand, John:
* rediscovered that the Standard Model group is SU(3) x SU(2) x U(1) divided by a certain Z_6 group
* rediscovered that 16 of spin(10) is a good representation for a single generation of quarks and leptons - i.e. rediscovered one reason behind grand unified theories
* rediscovered that manifolds with SU(5) holonomy are called Calabi-Yau five-folds
* wants to study, for a very incomprehensible reason, manifolds whose holonomy coincides with the Standard Model gauge group
The last point seems completely crazy because holonomy is exactly the symmetry - a part of the tangential group - that is broken by the manifold’s shape, while the gauge group of the Standard Model is a group that must be, on the contrary, completely unbroken.

Josh1, I hope you retract this unsavory suggestion that Peter Woit is tinkering with what his guests write at his blog. that is a lot more serious right now, I think, than the actual words or the difference in tone which is maybe not even worth arguing about. Could you possibly have made a mistake, Josh, and misremembered? Hmmm? Or confused this with some similar post by Lubos that he posted not on Woit blog but somewhere else?

 

[josh1]

Here is Lubos Motl's quote from the comments on Peter Woit's Not Even Wrong discussion of John Baez's paper:

"wants to study, for a very incomprehensible reason, manifolds whose holonomy coincides with the Standard Model gauge group

The last point seems completely crazy because holonomy is exactly the symmetry - a part of the tangential group - that is broken by the manifold’s shape, while the gauge group of the Standard Model is a group that must be, on the contrary, completely unbroken"

On his own blog, Lubos does not use the term "completely crazy". He uses the term "rather unnatural".

Now let's see if “rather unnatural” is appropriate.

But in Baez's discovery, there is no such implication. He specifically does NOT state just what role his manifold does or should play in the standard model. Therefore there is no obvious link from the symmetry breaking to the requirements of the standard model.

But Baez posted his paper in the physics section, not the math section. So I can only assume – as lubos did - that Baez feels this might have physical significance. But what other type of link then one between holonomy and the standard model could Baez possibly have in mind?

In the context of string theory the breakng of the symmetry is a breaking of spacetime symmetry since the Calabi-Yau manifolds there are precisely carriers of the spatial dimensions beyond three.

Elaborating a bit, this has to do with the role of symmetry breaking on the tangent space of the Calabi-Yau manifold to produce low energy phenomenology with the right characteristics. In this case it’s the spacetime characteristics that are being dealt with. Specifically, we require in four spacetime dimensions that there be only one unbroken supersymmetry. Now, 2n-dimensional Calabi-Yau manifolds begin life with O(2n) holonomy. For us, their key property is that there always exists a ricci-flat metric (so that there is zero torsion) that breaks this down to SU(n) holonomy. The reason that this is key is that it’s just the condition for d=4 N=1 supersymmetry.

Our first example of unnaturality then comes from the fact that the symmetry group of the standard model is a gauge group that describes only the physics of internal charges, but holonomy on the Calabi-Yau manifolds has nothing to do with this.

Our next example of unnaturality is that the holonomy was broken by simply choosing the right metric. But symmetries in the standard model are broken spontaneously by nature.

In relation to this, note that by definition, the gauge group of the standard model, since it’s supposed to represent grand unification of the nongravitational interactions, must not be obtained by spontaneously breaking symmetries of a larger enveloping group. This is because spontaneous symmetry breaking is a real physical process so that the larger group would by definition be the GUT gauge group and would predict new physics beyond that of the standard model.

The foregoing should make it quite clear that from a physical point of view the idea that the standard model gauge group should coincide with the holonomy group is indeed rather unnatural, and that I believe is what lubos meant.

 

[selfAdjoint]

And by the way, Josh1, since you apparently can read Lubos Motl's mind, is it perhaps true that you ARE Lubos Motl under your handle?

 

[josh1]

And by the way, Josh1, since you apparently can read Lubos Motl's mind, is it perhaps true that you ARE Lubos Motl under your handle?

Heh, heh, heh. Let's just say that I think I may now know what lubos motl must feel like a lot of the time. (Though, unlike him, I think LQG etc is still worthwhile. Although I must say that peter woit is no better when it comes to string theory. At least that's my opinion).

Anyway, I thought that what you meant was that you'd read a quotation by peter woit of what lubos said. I didn't understand that lubos himself had posted on peter woit's blog that he thinks what Baez was doing was completely crazy. So I can`t support lubos in that remark.

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[Juan R.]

Quoting your own website isn't providing evidence. Do you have any substantive links to support this claim?

I was NOT quoting 'own website'. It is clear that i am quoting

Radiation Physics and Chemistry 2004, 71, 611–617:

The highly accurate measurements of hydrogen and helium, mentioned above, are also in strong disagreement with current QED theory.

 

[selfAdjoint]

Now, 2n-dimensional Calabi-Yau manifolds begin life with O(2n) holonomy. For us, their key property is that there always exists a ricci-flat metric (so that there is zero torsion) that breaks this down to SU(n) holonomy.

And as it turns out, Baez, as a mathematician knows this and uses it. He states: "For any subgroup $$G \subseteq O(n)$$ let us say that an n-dimensional Riemannian manifold X is a G-manifold if the holonomy group at any point $$x \in X$$ is contained in G. Some examples are familiar:

• A U(n/2)-manifold is a Kahler manifold.
• An SU(n/2)-manifold is a Calabi-Yau manifold."

--So like Nakajima he cuts to the chase and just defines SU(n/2) as the holonomy symmetry of a Caslabi-Yau. (BTW, his n is the real dimension, that's why all those n/2 s appear).
He goes on,
"Which manifolds are G-manifolds when G= SU(3) X U(2) regarded as a subgroup of O(10) as above? The answer is simple:
Proposition 1. A G-manifold is the same as a 10-dimensional Calabi-Yau manifold X each of whose tangent spaces is equipped with a splitting into orthogonal 4- and 6-dimensional subspaces that are preserved both by the complex structure $$J_x:T_x X \rightarrow T_x X$$and by parallel transport.