The wrong turn of string theory: our world is SUSY at low energies

mitchell porter

Summary and prognosis:

Hadrons for the first n flavors have an approximate SU(2n) symmetry called "spin-flavor symmetry". Here you may see De Rújula, Georgi, and Glashow employing first SU(6) spin-flavor symmetry (u,d,s) and later SU(8) (u,d,s,c) to explain hadronic properties.

As mentioned in Catto 2003 (page 5), as well as separately possessing spin-flavor symmetry, mesons and baryons also share a common universal ratio of mass-squared to spin (this is the "Regge slope"). Miyazawa proposed that they might be placed into a single symmetry multiplet, but to do this he had to anticipate supersymmetry, since mesons are bosons and baryons are fermions. He extended SU(6) to SU(6|21); this was the real beginning of "hadronic supersymmetry".

The most commonly believed explanation of this, within QCD, appears to be that a meson is a gluonic string connecting a quark and an antiquark; and that inside a baryon, you end up with two quarks on top of each other at one end of a gluonic string, and with the third remaining quark at the other end; and that this structural similarity accounts for the shared Regge slope. This is the picture that Lichtenberg and Catto employ; and Nobel laureate Frank Wilczek is a fan of the "diquark" concept.

However, there is an alternative way to get meson-baryon degeneracy in a string theory, and it rests on a different, equally simple picture. Instead of a baryon being a string connecting a quark and a diquark, it's a string with a quark at either end and a third quark smeared along the string. In other words, the string itself is a fermionic string.

I think this, and the holographic approach to QCD, and Type II string models where all the standard model particles are open strings stretched between branes, together provide a context where the viability of Alejandro's idea can be explored. Holographic QCD can encompass diquarks, so it may not even be necessary to regard the two approaches to hadronic supersymmetry as mutually exclusive. The extension to leptons is a lot more problematic, but I think we have here a set of tools flexible enough to explore many variations on the idea, but rigorous enough to ensure that questions do have unequivocal answers.

tom.stoer

The problem is that up now it's only algebra w/o any fundamental dynamics. It looks like a bottom-up approach, but I can't see if this will produce something like a dynamical theory - or perhaps it may - but this will then be some sort of string theory again.

Regarding gravity: w/o gravity there is no need for string theory as far as I can see; string theory requires SUSY + additional dimensions - which we do not see in nature. String theory seems to be kind of framework to "produce theories as something sitting on top of vacuum states". OK, this is nice but afaik there's no additional benefit. w/o gravity it seems that string theory is nothing else but a very complicated "dual reformulation" of a huge class of (SUSY) gauge theories.

That's the reason why I am not very much impressed.

S.Daedalus

Also, leaving the top out is like letting the fat kid not play ball, which conjures up unpleasant childhood memories for me.

(More seriously, though, this is interesting speculation that I unfortunately probably won't have the time to fully familiarize myself with. There seems to be just enough fuzziness such that things might end up being merely a coincidence after all, if a suggestive one. Also, I'm unclear about the mass scales -- do the proposed superpartners have the same masses?)

arivero

And in fact one can go directly with susy without arguing about string theory, but still my feeling is that the algebra will have its origins from strings, at the end.

One could say that the coincidence for charged leptons is trivial, as it follows from the coincidence for quarks: given p,r quarks, the number of charged mesons of a kind is also p*r.

My hopes for leptons are based in some hints: One, that for neutral mesons it works only for the p=2 r=3 solution, ie the total of neutrals in SU(p+r) is (p+r)^2 - 2p*r -1, and it is a very happy think that oscillations have doubled the number of neutrinos from Weyl to Dirac. Two, that we have the muon at the same scale that QCD and particularly very near of the pion. And three, that the theory of Koide predicts the charged leptons from a quantity amazingly close to QCD "current quark mass". Of course there is some tension between this and the second point.

arivero

It is more as, the fat kid will be the goal keeper. And indeed unpleasant.

Hey, I think you have explained why topcolor and ETC (extended technicolor) theories are dismissed in favour of Higgs mechanism... the Higgs mechanism does not have any particular role for the top. But then it fail to explain why [itex]y_t=1[/itex]

What happens is that it is broken, but only mildly broken. And then all of the phenomenological work we have is not useful to us, because it is done on the assumption that the break is huge enough to hide the scalars up in the TeV scale.

arivero

No problem about it been a string theory, we were not telling that the wrong turn was to do strings, the wrong turn was to do "elementary Planck scale strings". And yes it is only algebra and we could do it without referring to strings nor dual models. But it does not seem to me an fuzzy or ad-hoc algebra. Let me review all the steps and what do we get in each.

1. We postulate that some number [itex]r[/itex] and [itex]p[/itex] of two kinds of particles, call them A and B, must form equal number of combinations of kind AA and kind AB.
   
   There is no loss of generality. The number of combinations AA is [itex] r (r+1) / 2 [/itex] and the number of AB is [itex]r p[/itex], so equality implies that
   
   [tex]r= 2 p -1[/tex]
   
2. For the abelian U(1) charge, there are two posibilities: either A=0 and then AB has equal charge than B; or A not zero and then AA must be -B and AB=-A. In the first case the charged leptons have charge B, in the second case they have charge 3A. Note that the first solution is not really valid because AB should be an antiparticle, but I mention it because it is very similar to the exotic quark assignment found by anomaly arguments. With the second solution, we conclude that the A quarks are down quarks, and the B quarks are up quarks. We conclude that there are [itex]p[/itex] quarks of type "up" and [itex]r= 2 p -1[/itex] quarks of type "down".
   
3. Note that for the total of combinations to be an even number -to do pairs of scalars- then [itex]p[/itex] itself must be even (because [itex]r[/itex] is always odd). So the minimal solution is [itex]p=2[/itex] [itex]r=3[/itex] and they produce six equal scalars and thus three generations of them.
   
4. The number of charged "sleptons" of a given charge is [itex]p r[/itex] too, so always equal to the number of "down" type "squarks". No surprises here
   
5. The number of neutral "scalarleptons" is, from SU(p+r) and substracting the charged ones, [itex](p+r)^2-1-2pr[/itex]. Asking it to be not two but four times the number of generations, we have
   
   [tex] (p+r)^2-1-2pr = 2pr [/tex]
   so that [tex](p-r)^2 = 1 [/tex] and the only solution compatible with the quark sector is the minimal solution.
   

What about the combination BB? Where, there are [itex]p (p+1) /2[/itex] of them. For the above solution, it means three of each BB type. On other hand, the gauge part of the Supersymmetric Standard Model has six scalars in the W and Z supermultiplets. My guess is that the combination BB can not partner to three generations of Dirac particles and because of this it is somehow blind to vector-like charges, ie blind both to colour and electromagnetism, while it can see the chiral charges (hypercharge and perhaps SU(2)). Not seeing color, there is only three BB (uu, uc, and cc) and three antiBB, and then they would match with the above six scalars. This impression of mine comes with some extra support from the p=16 example I spoiled in #15 before, where the "BB" combination also had a role related to symmetry breaking (between SO(32) and SO(16) or between E8 and E7).

mitchell porter

Let's look at this from another angle. Is the essential idea that all the sfermions (squarks and sleptons) are actually diquarks and mesons? Please correct me if that overlooks something - I have really struggled to get the idea straight in my head - but I think that is the qualitative essence of the proposal.

arivero

The strong version of the idea is as you describe. There is also a weak version, that the Supersymmetric Standard Model has a hidden global SU(5) symmetry, but this weak version is irrelevant here.

And there is a stronger version: that all the scalars of the Supersymmetric Standard Model are actually diquarks and mesons. This version needs more handwaving, because it involves some play with chirality, Dirac vs Weyl, etc. But in this version, also the scalars that give mass to the W and Z should be a peculiar kind of diquarks, build from the uu uc cc combinations.

mitchell porter

So far I have three ideas for how to realize this:

1. Look for a supersymmetric preon model in which this is a residual trace of supersymmetry among composite particles.

2. Look for a version of the supersymmetric standard model in which there is an emergent extended supersymmetry. It has to be an extra supersymmetry because in the SSM, by definition, the superpartners of the fundamental fermions are fundamental sfermions, not QCD composites, so if certain QCD composites are also superpartners of the fundamental fermions, it has to be a different supersymmetry.

3. Look for a "less than minimal" supersymmetric standard model, in which the only supersymmetry is the postulated relation between fundamental fermions and QCD composites. This is the fuzziest idea. It could involve looking for a hidden supersymmetry in the standard model itself, or for a hidden trace of supersymmetry in a supersymmetric theory broken to the standard model.

mitchell porter

I have identified a class of models which seem ripe for the inclusion of "lepto-hadronic supersymmetry" (LHS): single-sector gauge-mediated supersymmetry breaking models, especially when approached holographically. There's too much to sum up now, but see talk by Kachru, papers 1 2 by Kachru and others, talk by Gherghetta, paper by Gherghetta (especially part 7).

These papers are all written under the usual assumption that the superpartners of the known particles exist at high energies, and the model-building choices reflect the interaction of that assumption with various other conventional assumptions about how the world works. So implementing LHS in this framework will necessarily subvert some of the model-building choices which are standard in this literature. But it really looks like it could be done!

arivero

Hey, really I am enyoing these talks. With things as gauge bosons involved in susy breaking, and compositeness for al the quarks except the top, it sounds very much as if they were following research lines near to the conjecture here, even to the "strongest version".

Also, it seems it is a hard job. Damn, give me another five years.

mitchell porter

Let's look at this from a simple angle again. One version of what we're looking for would be a theory where hadrons are quarks bound by gluons, and where leptons are gluinos bound by squarks. Two immediate problems: there ought to be quark-gluino bound states too, and there ought to be leptonic resonances. How hard are those problems to fix, and are there other obvious problems?

arivero

I am not sure if it is the same theory, because I am not sure about how to describe leptons and quarks. I am intrigued that the QCD strings is inherently a bosonic string; can we build an extended string out of a fermionic field? I'd say no. Can we find a superpartner to the QCD string?

tom.stoer

Sorry to say that, but I still don't understand why the SUSY explanation shall provide any benefit. It adds new and un-observed particles (and perhaps resonances / bound states). It adds new questions and nearly no answers. It seems to be a solution hunting for a problem b/c there is no problem in QCD, we perfectly understand its structure.

mitchell porter

As far as I'm concerned, the question is: Is there a supersymmetric theory which gives us the standard model, and in which the numerical coincidences which Alejandro has noted, actually arise from supersymmetry? Alternatively, can we prove that no such theory exists? If it can't be done, it would be good to understand why.
This is a basic question about how supersymmetry works in theories like super-QCD, to which I do not know the answer. Supersymmetric theories are diverse and very complex. For example, my earlier remark about "gluinos bound by squarks" was rather naive; it looks like the most important interactions of gluinos are with gluons. In discussions of MSSM, you will find people saying that the superparticles will in any case decay to ordinary particles, so composites would not be stable, but that is under the usual assumption that they must be too heavy to have been seen already. So among other things, one should probably look at the behavior of massless super-QCD first - a theory which already comes in many forms: "pure SQCD" with no quarks; SQCD with adjoint quarks, SQCD with quarks in the fundamental representation; SQCD with various numbers of flavors and colors. The 1990s results of Seiberg on electric-magnetic duality look to be of basic importance in understanding these theories.

In all these theories, massless and massive, the elementary fields can be arranged into superfields. But what about composite objects like mesons and baryons - are they generically part of supermultiplets as well? This is what I don't understand. By the way, Seiberg's duality involves the appearance of an extra meson superfield on one side.

Back in comment #18, I mentioned a minor research program from string theory - "orientifold planar equivalence" - in which meson strings have baryon strings as superpartners. In the baryon string, the third quark is smeared along the length of the string. See these lectures by Armoni (they also appeared in Nucl Phys B, but not on the arxiv). In the third lecture, pages 12-13, Armoni actually mentions quark-diquark supersymmetry (Lichtenberg's hadronic supersymmetry), and says this is an alternative explanation (he explicitly says that a certain fermion in N=1 SYM becomes superpartner of the meson). Though I wonder if this picture, with the third quark smeared along the string, might arise from a symmetrized version of the quark-diquark string.

Anyway, obviously we need to look at this and see if it can be extended to include your extension of hadronic supersymmetry to leptons. The framework is unfamiliar to me ("type 0' string theory") so I don't know what pitfalls lie ahead.

arivero

The whole "program" is to have less un-observed particles that in standard susy (as in the MSSM). On one side, you know that the the minimal SSM is smaller that the MSSM by two scalars, at the cost of not having a higgs mechanism. On other side, you can arrange all the scalars of this SSM using a SU(5) based flavour symmetry with seems very much as QCD with five flavours. The goal is not to understand QCD, the goal is to understand this flavour and see if it allows a formulation in terms of gluon-like composites, so that the total of particles in the "sBootstrapped SM" is still less than in the SSM.

Even if we understand QCD, we dont understand yet ETC, ie the multiple reincarnations of topcolor and extendedtechnicolor that could be still around the corner in CERN (and Fermilab!). So there is a benefit even if you dont buy the whole program.

tom.stoer

OK, I'll try to get that