Exploring Pros & Cons of SUGRA

[arivero]

Forking from the poll https://www.physicsforums.com/showthread.php?t=338150 I would like to collect oppinions for and against SUGRA, and specially motivations.

One of them is that it seems to have enough room for the known fermions. This was stressed by my old boss in
http://arxiv.org/abs/0808.3667
and perhaps it could be also reflected in the E8 ideas https://www.physicsforums.com/showthread.php?t=196498 https://www.physicsforums.com/showthread.php?t=202439

Let me stress one of the main points in the textbooks, that while the gravitino has the 128 degrees of freedom of a full Rarita Swinger fermion, the graviton has only 44. So we need to add 84 scalars to the theory.

It is tempting to think that there ara 84 electrically charged sfermions in the susy Standard Model. But then the sneutrinos (12 of them), the gauginos (24 degrees of freedom) and the 4D gravitino (2 degrees?) should go to the other 44, leaving only 6 for the higgsinos. If on other hand we use 8 degrees of freedom for the two higgsinos of the MSSM, the 4D graviton and gravitino must me left out!

 

[arivero]

to add some references:

As a placeholder for SUGRA
PPT slides from Lance Dixon's Erice 2009 talks:
31 August: http://www.ccsem.infn.it/issp2009/professors/Dixon-I.ppt
1 September: http://www.ccsem.infn.it/issp2009/professors/Dixon-II.ppt

The most interesting thing I get from these references is that they seem to use the "squaring" of N=4 Super Yang Mills to get N=8 Sugra. Of course 16^2=256, but how does it fit with the 11D (or 10D) point of view?

 

[Thomas Larsson]

Arguments for and against SUGRA are really arguments for and against SUSY. SUSY + gravity implies SUGRA, and I don't think that I have to argue for gravity.

The main argument against SUSY is that it doesn't seem to be there. Whereas the final verdict will have to wait some more years, one can note what Frank Wilczek wrote in his Future summary from 2001, http://arxiv.org/abs/hep-ph/0101187 :

"...predicts a relatively light Higgs particle. The upper bounds extend to 130 Gev or so, but they are not easy to saturate, and I’d be happier with 115 Gev." (p 7)

The Tevatron will be there in a couple of years.

"it will not be easy to reconcile limits tau_proton >= 10^34 yrs. with straightforward models" (p 19)

Question: Where is SuperKamiokande now?

"Of course, the ultimate test for low-energy supersymmetry will be to produce some of the predicted new R-odd particles. Even in the focus point scenario, there must be several accessible to the LHC." (p 20)

When LHC reaches design energy is anybody's guess.

 

[arivero]

The main argument against SUSY is that it doesn't seem to be there.

Ah

It does not aply in my particular case, remember that I believe it that the charged pion is a partner of the muon :-D. But yes, speaking for the orthodoxy it seems it is not there. The worst problem, to me, are the gauginos. Gluinos can be confined, but the photino should be there.

 

[arivero]

and I don't think that I have to argue for gravity.

It could be interesting to argue against.

Point is, the MSSM contains, looking degrees of freedom, 128 bosons + 128 fermions:

quark and leptons: 96 fermionic , and then the same number of squarks
gauge fields: 24 bosonic, and then the same number of gauginos
higgs fields: 8 bosonic, and then the same number of higgsinos.

The unique D=11 SUGRA also contains this same number of degrees of freedom. It is a pity that when going down to D=4 we need to reserve 2 of them for the graviton (and 2 for the gravitino, of course).

Moreover, the patterns of D=11 SUGRA and its D=10 descendant have some numerological ring of the patterns of the standard model. In D=11 sugra there is only a fermion field, having all of the 128 fermionic degrees of freedom. But it has two bosonic parners, amounting to 44 and 84 degrees of freedom. We could think of the 84 as the number of charged quarks and leptons. Then, when we descend to D=10, IIA, the 44 divides in 35+8+1, but the 84 divides nicely in 56 + 28, and the number of charged fermions (quarks and leptons) in one generation is also 28. We do not see explicitly the neutrinos in this structure, but it is OK because these SUGRA are non chiral, so we should not expect to see them.

So one is left wondering if it is compulsory to get 4D gravity from D=11 SUGRA. It could be easier to get the MSSM.

 

[arivero]

We could think of the 84 as the number of charged quarks and leptons

Sorry I had not noticed this: we could forget about charge and thing about mass. There are 84 light "fermions" in the standard model, the top having the other 12 "fermions". So other speculation could be that the top is massive because in 11D it is forced to pair with the graviton.

Really the same argument was working before for the neutrino, but for its "majorana" mass, which is huge if we want to believe in the seesaw. The point is that in 11D, there are 12 degrees of freedom of the fundamental spinor which are forced to pair with the graviton. We could use them for the three neutrinos, or we could use them for all the three colours of the top quark.