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

A problem I still dont get about relating gluons to strings is that the QCD string is not a single gluon state... the QCD string appears at long distances and intuitively it seems as a "classic field". But a classic field is a collective of elementary excitations; it is because of it that force fields are always bosons, is it not? It is not easy to build a collective field out of fermions (note that a fermionic field, at least in 3d, is proportional to hbar: it dissapears in the classical limit).

 Quote by mitchell porter 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. (...) 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.
 I want to tackle your idea, alluded to in comment #7, that the QCD string could be the Type I fundamental string; an idea arising from the 1987 paper by Marcus and Sagnotti, in which the SO(32) group of the Type I theory is derived by placing 5 "quarks" (and their antiquarks) at the endpoints of the string. For anyone just tuning in, the logic of the idea, explained in the first link above, is that the top quark decays too quickly to form hadrons, so all the mesons we know about are only formed from the first five flavors. Although the idea of weak-scale superstrings exists, I think this is the least likely avenue (mentioned so far) towards a realization of very-low-energy supersymmetry. But it might be instructive to walk a short distance down this road, and see what there is to discover. So, to begin, here's a modern exposition of Type I string theory by Lubos. The Type I theory is just Type IIB with a space-filling orientifold plane, and then you also need 16 space-filling D-branes and their images reflected in the O9-plane in order to cancel anomalies. 16+16=32 and you can almost see where SO(32) comes from (and a similar relation holds in the S-dual heterotic SO(32) theory). I say "almost" because I'm used to a stack of n D-branes giving rise to a SU(n) theory, not a SO(n) theory; I suppose the O-plane has something to do with the latter. So what's going on in Marcus and Sagnotti's paper? I have put together an explanation, a crucial part of which came from section 3.3 of the thesis of Sven Rinke (which was turned into a book). The fundamental issue is how to obtain the "Chan-Paton factors" which contribute to the amplitude when you have strings ending on branes. When M&S wrote their paper, it wasn't even understood that there are branes in the Type I theory, so they came by their construction another way. But in Rinke I read that, normally, the Chan-Paton factor is obtained from a Wilson line in the worldsheet theory of the brane(s) to which the string is attached, a Wilson line which follows the path of the string endpoint. The method of M&S is an alternative, in which you have fields living on the endpoints and the Chan-Paton factor comes from including them in the path integral. They are called boundary fermions and they have had a revival in recent years, including an application in Berkovits's pure spinor formalism. Along with the space-filling D9-branes, the only stable branes in Type I string theory are D1-branes and D5-branes. I had thought that maybe I could find a braney explanation of why M&S needed five pairs of boundary fermions (quark, antiquark being one pair) in the D5-branes: open strings in Type I can end on the D1s and D5s as well as on the D9s, so there's a calculus of Chan-Paton bookkeeping which extends to those lower branes as well. But I haven't done the work to understand it yet. You can read about some of it in section 14.3 of Polchinski volume 2.
 Alejandro, what's your philosophy regarding the Higgs?

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 Quote by mitchell porter Alejandro, what's your philosophy regarding the Higgs?
That the Higgses coming from the algebra are reasonable, but the ones coming from the dynamics are dubious.

If you look at the SUSY algebra, you will see that in order to build massive supermultiplets, one must add an extra scalar for each massive particle. This can be seen by construction with the susy operator, but you can also check it directly by counting: get a massless Z0; it can be partnered with a Weyl spin 1/2 fermion and it makes a fine gauge massless supermultiplet. But now if you want the Z0 massive, you have an extra bosonic helicity, you need to counterweight in the fermion side and the minimal thing you can do is to add another Weyl spin 1/2 fermion (I guess you could also try to go up to spin 3/2, in any case the counting is the same), but then you have added two fermionic degrees of freedom, so now you must add an extra scalar in order to counterweight exactly.

So a massive Z0 implies an extra scalar, and same for massive W+, W-. That comes from the algebra, it is true for any SUSY setup, and I think that these "higgses" should be there in some disguise. Now, the minimal dynamics of MSSM goes further: it needs to use full SU(2) Higgs multiplets. so it adds another two bosons to the total count. These bosons are, in my opinion, not a real requisite, they come from a very particular model.

As for the "disguise" of the higgses in my own construct, we can discuss it, if you want. But note that the above applies to any SUSY model, not just mine.

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 Quote by arivero (I guess you could also try to go up to spin 3/2, in any case the counting is the same)
Well, not exactly the same. If you want the 3/2 fermion to be massive, you need double again, while in the other case you can use both Weyl 1/2 to build the massive dirac fermion. But I mentioned it because the solution where two d.o.f come from an 1/2 and the other two come from a 3/2 has a peculiar content, close to some compactifications of maximal sugra.

 Quote by me again As for the "disguise" of the higgses in my own construct, we can discuss it, if you want.
Really, the only idea is that you could have noticed that after the full (and exact) pairing for $\pm 1,0, \pm 2/3$ and $\pm 1/3$, there are still six combinations left, uu, uc, cc and their antiparticle versions. I can not use them to make Dirac fermions, and then I suspect that these combinations are chiral in a way that they can only couple in an axial way: they can not see QCD, and they can only see EM in the way it comes from SU(2) and hypercharge.

With respect to my comments #29 and #32, this paper looks exciting (I haven't read it yet, and I'm posting about it, that's how exciting): It's about how to obtain QCD as a limit of super-QCD, and it actually talks about the meson states of QCD. This is what's missing in all the literature on supersymmetric preon models. Over 100 papers talk about "composite superfield" or "composite supermultiplet", but they never bring standard model mesons into these supermultiplets, they only talk about quarks and leptons.

Here's what they (Sannino and Schechter) say:
 At the fundamental gauge theory level the supersymmetric theories contain gluinos and squarks in addition to the ordinary gluons and quarks. At the effective supersymmetric Lagrangian level, all of the physical fields are composites involving at least one gluino and one squark. This means that none of them should appear in an effective Lagrangian for ordinary QCD. Where the mesons and glueballs, which are the appropriate fields for an effective QCD Lagrangian, actually do appear are in the auxiliary fields of the supermultiplets, which get eliminated from the theory... The simplest approach to relate the supersymmetric (SUSY) effective theories to the ordinary ones is to add suitable supersymmetry breaking terms... The standard procedure assumes the breaking terms to be ‘‘soft’’ in order to keep the theory close to the supersymmetric one. Indications were that the soft symmetry breaking was beginning to push the models in the direction of the ordinary gauge field cases. However the resulting effective Lagrangians were not written in terms of QCD fields. In this paper we will provide a toy model for expressing the ‘‘completely broken’’ Lagrangian in terms of the desired ordinary QCD fields. Since we will no longer be working close to the supersymmetric theory we will not have the protection of supersymmetry for deriving ‘‘exact results.’’ In practice this means a greater arbitrariness in the choice of the supersymmetry breaking terms. The advantage of our approach is that we end up with an actual QCD effective Lagrangian.
"Mesonic superfields" show up in Part III. This seems really promising, because it's an analysis at the level of a Lagrangian, and not just talking about quantum numbers.
 Equations 3.2-3.4 in that paper are something to stare at, especially if you're a supersymmetry novice. But let's try to interpret them with some very basic help. All the "F"s are complex scalar auxiliary fields which allow the supersymmetry algebra to close off-shell (see chapter 3 here). One normally considers only "phi" to be the scalar superpartner of the fermionic "psi", with "F" left out in the cold, but here the physical meson fields are being found inside an "F". Also, the plan in the paper is to completely decouple the superpartners of the known particles, leaving just QCD, so they want everything except the third term of equation 3.4 to drop out. But our objective is to identify some of the leptons with superpartners of those mesons, so presumably we want to keep some or all of "psiT". What if we get "FQ" to drop out? "psiT" is "quark times antisquark plus antiquark times squark", and we also still have scalar squark-antisquark composites in the picture, alongside the mesons. It seems a little messy. But if we boldly ignore all the details, the message seems to be that a lepton, in this scheme of things, will be "quark times squark". Now maybe that particular approach makes no sense in any possible world. But I can begin to imagine that, in a more complicated scheme, such considerations would allow you to construct a working preonic model, in which leptons are composite and their superpartners are mesons or diquarks. Meanwhile, let me also note the existence of some papers by Kyianov-Charsky (also spelt Kiyanov-Charsky and Kiyanov-Charskii), in which QCD mesons and baryons are similarly derived from super-QCD, with the explicit intention of realizing hadronic supersymmetry: 1 2 3.
 Blog Entries: 6 Recognitions: Gold Member A differente venue: http://arxiv.org/abs/0909.5430 "SUSY Splits, But Then Returns", by Sundrum, refers to some previous works (ref 12, 13) on emergent supersymmetry. It would be very surprising if some of these models, which are proposed at the level of toy models, at the end happen to be so accuratelly reflected in Nature.
 Update on the bottom-up and top-down strategies: 1) There are a number of papers on expressing the Nambu-Jona-Lasinio model (1 2) in terms of diquark and meson variables. Perhaps see especially "PNJL", the combination of NJL with the "Polyakov loop". There is also a supersymmetric version (sometimes called super-NJL), which one could try to re-express in this way. Also, early papers of Tomohiro Matsuda try to apply NJL to SQCD. 2) "E6 diquarks" are one of the exotic particles that have failed to turn up at the LHC - but I think these are vector diquarks. Nonetheless, if you visit the 1989 review article on string E6 models (still frequently cited), and view the discussion on pages 199-200, about leptoquark, diquark, and quark couplings in the superpotential... there might be some guidance there, for how, say, a super-NJL model might embed into a theory with leptons. (Also see NJL from branes. Can it be combined with holographic diquarks?)
 Blog Entries: 6 Recognitions: Gold Member I got an email from Bernard Riley telling that also him, back in http://vixra.org/pdf/1004.0101v1.pdf, got worried about the point of having spin 1/2 and spin 0 particles with very near masses, say muon and pion etc. Again, it is beyond all belief that two different mechanism of mass generation (SU(3) colour versus Yukawian Higgs) without any relationship between them, and coming down from mass planck scale, at the end produce a value with a difference not beyond a 10%. The problem is that there is no dynamics unifying both mechanism... So the reports of Mitchell are interesting, they indicate that is could be possible to build some mechanism, after all.

 Quote by arivero I got an email from Bernard Riley telling that also him, back in http://vixra.org/pdf/1004.0101v1.pdf, got worried about the point of having spin 1/2 and spin 0 particles with very near masses, say muon and pion etc. Again, it is beyond all belief that two different mechanism of mass generation (SU(3) colour versus Yukawian Higgs) without any relationship between them, and coming down from mass planck scale, at the end produce a value with a difference not beyond a 10%. The problem is that there is no dynamics unifying both mechanism... So the reports of Mitchell are interesting, they indicate that is could be possible to build some mechanism, after all.
Hi Arivero,

Good, you are back again. I send you a PM (some days back)regarding the mass of the proton and electron and they are linked to a thread you started. the equations almost look identical to the one you posted, so they must be related. I don't mind if you don't see any value in them but I will be just happy with a two letter word ,like ok, reply to acknowledge recieving the info. Mitchelle has been kind and has taken a look at them.