Exploring D=9 Supergravity and SU(3)xU(1) Non-Chiral Theory in Four Dimensions

[arivero]

I want to do a Kaluza Klein exercise but I am afraid I am too lazy to finish any work if not under pressure. So I was thinking, perhaps it could be done here, collaboratively, and signed by all collaborators (the ones wishing/willing to sign; others can be just acknowledged or even remain anonymous )

The topic is Kaluza Klein in D=9. The immediate goal, to derive a SU(3)xU(1) non chiral theory in four dimensions. The secondary goal, see if the matter content can be related to D=9 supergravity, whose Rarita-Schwinger fermion has 48 degrees of freedom (half of the Standard Model content)

Some references on D=9 sugra:
http://arxiv.org/PS_cache/hep-th/pdf/9802/9802138v1.pdf
http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?198412163

 

[ZapperZ]

Is it possible (or even, more appropriate) for something like this to be done in the IR forum?

Zz.

 

[benk99nenm312]

I think the problem is more about purpose. Why go for only half of the Standard Model?

 

[Count Iblis]

Is it possible (or even, more appropriate) for something like this to be done in the IR forum?

Zz.

Why not do it here? It would be fun to publish a paper in PRD that has "Physics Forums" as the author. Arivero will be corresponding with PRD on our behalf, he will copy and paste the Referee reports in this thread.

 

[arivero]

Zapper, I will not oppose if you arrange to move elsewhere. I can also move it to the blog. Point was, I was interested on the collaborative part: it is not my theory nor a off-road track; the goal was to follow orthodoxy (so the stress on "arxiv"). If during two or three weeks there is no brainstorm nor collaboration, I would frozen this thread and follow up in the blog.

I think the problem is more about purpose. Why go for only half of the Standard Model?

Because:
- It is an exercise.
- D=9 does not allow for the full Standard Model gauge group in Kaluza Klein modes. D=11 is needed for that and even in such case...
-... Odd dimensions do not allow for chiral fermions. So weak isospin and hypercharge, SU(2)xU(1), can not be expected to work.
- D=9 is the minimal dimension for colour plus EM, this is SU(3)xU(1), the two non chiral forces.

Edit: also, note that D=9 N=2 has two Rarita-Schwinger fermions.

 

[arivero]

Why not do it here? It would be fun to publish a paper in PRD that has "Physics Forums" as the author. Arivero will be corresponding with PRD on our behalf, he will copy and paste the Referee reports in this thread.

Actually the Editor reports I would be surprised if it filters to real referee cycle.

 

[Count Iblis]

Let's look ahead to the last post in this thread:

Dear Dr. Arivero

Your manuscript ``Kaluza Klein theory in D=9 " is being accepted for publication in Physical Review D. The formal notice of acceptance will be sent separately.



Dennis Nordstrom
Editor
Physical Review D

 

[garrett]

This is a neat idea. And it relates to something I noticed a few years ago, but never wrote up. You can actually reproduce all of the standard model gauge fields in D=8 if you're willing to include torsion. The way this works is, you choose $$\mathbb{C}P^2 = SU(3) / U(2)$$ as the KK part of the manifold, then the frame picks up a SU(3) from the Killing vectors and the contorsion gets a U(2) part. I think this works out to give a good action on spinor fields too, but it's kind of a mess, and the spinors are thrown in ad-hoc. The only somewhat bad thing one has to do is assume some unusual dynamics for the torsion in order to reproduce the usual gauge field dynamics for the U(2) fields. Also, it's fun to include the conformal factor of the KK space as an independent degree of freedom that can vary over spacetime.

If you start along this path, the calculations are long but straightforward -- there's nothing but a ton of index gymnastics standing between you and a nice expression for the effective action. I wish I had more time to work through it here, but I could check in every now and then and give comments.

 

[MTd2]

So, you are busy with the Hexality thing after several months of experimation? Can you say something new that you've found?

 

[arivero]

... in D=8 if you're willing to include torsion.
...and the spinors are thrown in ad-hoc.

Not sure if it is completely ad-hoc. As it can be seen in table 3 of document hep-th/9802138, D=8 has two supergravities, a N=2 with 128 physical degrees of freedom, and a N=1 with 48. As I said above, the SM fermions have 96 fermionic dof. On other hand, as LJ Boya pointed out a couple years ago, the full MSSM, including two higgses, has 128 fermionic degrees of freedom.

If we take the point of starting from a divisor of 96, our list is 48 32 24 16 12 8 6 4 3 2... In full representations, according table 3, the most interesting candidate could be D=8 with N=1.

If we are interested only on Rarita-Schwinger degrees of freedom, then its relationship with the number of dimensions is
11 128
10 112 (56)
9 48
8 40
7 16
6 12 (6)
5 4
4 2
(where in D= 2 mod 4 we can gain an extra halving) In such case, the most interesting dimension is D=9. It could be worthwhile to try SU(2)xU(1) in D=7 and plain SU(2) in D=6; in fact I suspect the later should be already reported in the literature.

In fact this already suggests a warming exercise. Given the counting of real components:

	bosons					fermions	
	grav.	antisimetrical tensors		r-s	spinor
D	e	abcd	abc	ab	a			
11	44	126	84	36	9		128	16
10	35	70	56	28	8		(56)	(8)      (note: also tensors can be halved!)
9	27	35	35	21	7		48	8
8	20	15	20	15	6		40	8
7	14	5	10	10	5		16	4
6	9	1	4	6	4		(6)	(2)       (as above)
5	5		1	3	3		4	2
4	2			1	2		2	2
3					1			1
2								1
1

- try different proportions in order to get the same number of fermions that bosons
- look for interesting patterns
- check them against table 3
- verify table 3 explicitly

Not so elementary: explain for each supergravity in table 3 how and when does it descent from dimensional reduction of the higher ones, and tabulate the decomposition process as the reduction proceeds. Example: how do you get D=10 spinors out of D=11 Rarita-Schwinger, and so on for each dimension.
__________________
http://dftuz.unizar.es/~rivero/research/

- look for interesting patterns

For instance, D=5 N=8 has exactly 96 spin 1/2 objects. Does it qualify for a mention? Deserves further work? Has it been already reviewed? Is it related to the goal calculation (D=9 N=1 or 2)?

 

[nrqed]

I want to do a Kaluza Klein exercise but I am afraid I am too lazy to finish any work if not under pressure. So I was thinking, perhaps it could be done here, collaboratively, and signed by all collaborators (the ones wishing/willing to sign; others can be just acknowledged or even remain anonymous )

The topic is Kaluza Klein in D=9. The immediate goal, to derive a SU(3)xU(1) non chiral theory in four dimensions. The secondary goal, see if the matter content can be related to D=9 supergravity, whose Rarita-Schwinger fermion has 48 degrees of freedom (half of the Standard Model content)

Some references on D=9 sugra:
http://arxiv.org/PS_cache/hep-th/pdf/9802/9802138v1.pdf
http://ccdb4fs.kek.jp/cgi-bin/img/allpdf?198412163

Neat idea but what would you put for Author? If it's only written Physics Forums, I think that most people will assume it is a prank and won't look at it. And if it does lead to something interesting, you would want to submit it to a journal. Then the issue becomes: what is the criterion for including or not someone's (real) name?

Sounds like a neat idea.

 

[arivero]

Then the issue becomes: what is the criterion for including or not someone's (real) name?

Contribution and willingness. The first in the sense of answering some point raised in the thread, so that the answer is incorporated to the paper. The second because someone could want to help but not be involved with names.

"Answering" is the key. At the current level, for instance, I myself have not yet qualified for inclusion.

 

[malawi_glenn]

I think the problem is more about purpose. Why go for only half of the Standard Model?

Well, you thought that positrons had negative rest mass, are you sure that you are the right person to ask for "purposes"? (and do you think that you can contribute?)

 

[benk99nenm312]

Well, you thought that positrons had negative rest mass, are you sure that you are the right person to ask for "purposes"? (and do you think that you can contribute?)

Of course not. I just wondered what you guys were up to.