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

[mitchell porter]

I want to tackle https://www.physicsforums.com/showthread.php?t=180275" 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 http://physics.stackexchange.com/questions/3342/space-time-filling-d-branes-in-type-i-superstring-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 http://gradworks.umi.com/32/71/3271005.html" ). 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.

 

[mitchell porter]

Alejandro, what's your philosophy regarding the Higgs?

 

[arivero]

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.

 

[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.

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.

 

[mitchell porter]

With respect to my comments #29 and #32, http://arxiv.org/abs/hep-th/9708113" 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.

 

[mitchell porter]

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 http://www.phys.columbia.edu/~kabat/susy/3plus1susy.pdf" ). 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 "psi_T". What if we get "F_Q" to drop out? "psi_T" 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: http://arxiv.org/abs/hep-ph/9501412" .

 

[arivero]

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.

 

[mitchell porter]

Two more ideas on how to construct a theory realizing "hadronic supersymmetry extended to leptons":

1) Do what Sannino and Schechter did (comment #40), but in reverse. That is, instead of beginning with a supersymmetric Lagrangian and judiciously adding symmetry-breaking and mass-generating terms until you get the standard model, start with the standard model and add terms until you have a broken supersymmetric Lagrangian. The tricky part is once again the aspect of this idea which is unconventional: the mesons and diquarks are the degrees of freedom which must enter into supermultiplets, so we may need to start with an effective field theory (for the whole standard model, not just for QCD) in which they appear directly in the Lagrangian.

2) Look for a realization of hadronic supersymmetry in a string phenomenological model, and then see if it can be extended to the leptons. The papers on "orientifold planar equivalence" that I cited earlier (comments #18, #32)) don't quite work here, because as I understand it they are just illustrative toy models, not real-world models. What I'm thinking here is that string phenomenology (so far as I can see) mostly contents itself with obtaining states which can correspond to free quarks and gluons at high energies. Mesons and baryons are a low-energy phenomenon and are left for field theorists to derive from QCD. But what do the existing accounts of hadronic supersymmetry look like if we restate them within the framework of a beyond-SM theory? We might get some clues for the extension to the leptons. (I suppose one could do this, not just for string models, but also for MSSM and SUSY-GUT.)

 

[mitchell porter]

Update on the bottom-up and top-down strategies:

1) There are a number of papers on expressing the Nambu-Jona-Lasinio model (http://en.wikipedia.org/wiki/Nambu%E2%80%93Jona-Lasinio_model" 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 http://www.sciencedirect.com/science/article/pii/0370157389900719" (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 http://arxiv.org/abs/hep-th/0604017" ?)

 

[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.

 

[qsa]

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 receiving the info. Mitchelle has been kind and has taken a look at them.

https://www.physicsforums.com/showthread.php?t=46055

 

[mitchell porter]

The paper where I first came across "diquark coupling" vs "leptoquark coupling" as a model-building choice was http://prd.aps.org/abstract/PRD/v41/i5/p1630_1" (1990). "We envisage a cascade mechanism, whereby quarks and leptons gain mass at various orders of perturbation theory from masses induced at the preceding order of approximation. In this way we hope to explain at least some of the qualitative features of the observed mass spectrum."

It has very few citations, especially in the past decade, but there is a recent one, http://arxiv.org/abs/0906.4657" ). "Radiative models of flavor have a long history...", and to prove their point, they list 17 papers (refs 19-35), starting with Weinberg in 1972.

At this stage, I have no idea whether such models provide guidance in the search for a theory realizing Rivero supersymmetry ;-) or whether the details of the masses is just a distracting complication. My basic notion of how to make it work is still SQCD with preons, so that e.g. the lepton-meson multiplet involves composite particles on both sides. But maybe it requires something more subtle, like Seiberg duality or holographic cascades.

 

[mitchell porter]

OK, I'm sold, it would be extremely stupid to be thinking about how to realize supersymmetry in this way, and to ignore the similarity of the pion mass and the muon mass. Instead, it's absolutely the best clue about how to do it, for the very reason you (Alejandro) state: the method of mass generation is supposed to be completely different.

Electron, muon, and tauon masses satisfy Koide's formula to high precision. Pion, kaon, and eta-meson masses satisfy a Gell-Mann–Okubo mass formula, but only approximately. I don't understand the https://www.physicsforums.com/showthread.php?p=1451883#post1451883" tries to do so.

Also, today's http://arxiv.org/abs/1106.3074" looks important. There is a good chance that we should be trying to take advantage of such relationships (e.g. as in the paper by Sundrum). But in all cases, the authors think of the superpartners as something additional to all the known particles. We need to somehow retrace their steps, but with the role played by supersymmetry entirely folded into the known, Standard Model particles.

edit: http://arxiv.org/abs/1010.4105" - a theory paper, which inspired the Seiberg dual for the MSSM, and which connects the chiral effective theory for QCD to Seiberg duality for SQCD - looks supremely important.

edit#2: How many supremely important papers can there be, I wonder?

http://arxiv.org/abs/hep-ph/0501200" :

"This paper could have been called 'Connecting Diquarks to Pions'"... The most solid consideration, albeit somewhat remote from bona fide QCD, is that based on SU(2)color. Reducing the gauge group from SU(3) to SU(2) allows one to relate diquarks and pions through a global symmetry which exists only for SU(2)color. Diquarks become well-defined gauge-invariant objects, which share with pions a two-component structure with a relatively short-range core. Then one can speculate, qualitatively or, with luck, semiquantitatively on what remains of this symmetry upon lifting SU(2)color to SU(3)color. It is worth noting that all instanton-based calculations carry a strong imprint of the above symmetry since basic instantons are, in essence, SU(2)color objects."

So here we have a symmetry connecting diquarks to mesons. Earlier, we had an interpretation of QCD mesons in terms of a supersymmetric duality. We also have a realization of this supersymmetric duality for the MSSM, in a way which extends to the W and Z. It remains only to decisively fold the leptons themselves into this circle of relationships.

 

[mitchell porter]

Now getting very close to a coherent field-theoretic thesis: We should be trying to generate the masses through a superconformal anomaly. The idea is that the pion mass is generated by a conformal anomaly (or at least breaks conformal symmetry in the chiral effective theory); and in "anomaly mediated supersymmetry breaking", squarks and sleptons acquire their masses from a superconformal anomaly; but in the scenario here, squarks are diquarks and sleptons are mesons. Maybe the answer is just SQCD + AMSB!

 

[arivero]

Mitchell, did you got your preprint online? If you wish, I can upload it somewhere, if only for google to find it...

 

[mitchell porter]

It needs more work.

 

[arivero]

btw I like the SQCD + AMSB line.

 

[arivero]

If Koide is a serious thing, then the clue is the value of the constituent quark mass, 313 MeV. The same mechanism that produces the mass of leptons should produce this mass,

Koide rule is that the mass of leptons is

313.188449 MeV ( 1 + sqrt(2) cos(phase))^2

The square is also inspiring, it seems as if the interesting quantity is actuall sqrt(mass).

 

[mitchell porter]

To make further progress, I feel the need to now return to the original hadronic supersymmetry, which is the prototype. The proposed correspondence for the leptons is just a matter of matching up the charges, but hadronic supersymmetry has a dynamical content, as requested by suprised in comment #11. It would be a big advance to embed the leptons in an extension of one of the effective theories with hadronic susy, even if the extension is dynamically trivial.

In comments #13 and #18, I mentioned Sultan Catto as offering a sophisticated approach to hadronic susy, and he's written some more in the past two years, though for some reason it's not on arxiv (you can find it at inspirebeta). I believe it's an extension of work with Feza Gursey from 1985 and 1988, on an octonionic superalgebra which contains baryons, mesons, diquarks, and quarks. The 1980s version also contained exotic hadrons (like tetraquarks, I guess), the new version does not.

At a more elementary level, I don't see Catto (or other advocates of hadronic susy) working with more than three flavors. So before we extend hadronic susy to the leptons, we may have to extend it to all the hadrons! And the first step in that direction may be to extend the purely bosonic part of hadronic susy - spin-flavor symmetry (see comment #18 in this thread) - to 5 or 6 flavors. I can find precisely http://arxiv.org/abs/hep-ph/0107205" talking (page 9) about SU(12) spin-flavor wavefunctions, and no-one at all talking about SU(10) (five flavors). These wavefunctions are employed in a "naive spectator quark model", and B.Q. Ma has a SU(6) quark-spectator-diquark model, so the road ahead is mapped out for us...

 

[mitchell porter]

Current thoughts: Mass is generated by anomalous breaking of superconformal symmetry in the strong interactions, which is then transmitted to the charged leptons (origin of the shared 313 MeV scale) and also to the electroweak gauge bosons. The whole standard model may have a "Seiberg-dual" description in terms of an SQCD-like theory with a single strongly coupled sector, with the electroweak bosons being the dual "magnetic gauge fields", and lepton mass coming from "technicolor instantons" in the electric gauge fields (analogous to the origin of nucleon mass in QCD).

This is a transposition of recent ideas, due to http://arxiv.org/abs/1106.4815" and collaborators, to the present context.

 

[arivero]

This is a transposition of recent ideas, due to http://arxiv.org/abs/1106.4815" and collaborators, to the present context.

Luty and Terning are doing a good work, at least preparing powerful tools... and students brainy enough to use them qhen they become needed after the runs of the LHC. I am sorry I am already old to retake all of these.

 

[mitchell porter]

I hope to have something to say soon about where the constituent quark mass scale comes from, but meanwhile, http://bajnok.web.elte.hu/JHW/programme.html#pomarol" has a nice basic explanation of the idea of "partial compositeness" which features in these Seiberg-like models.

 

[mitchell porter]

If Koide is a serious thing, then the clue is the value of the constituent quark mass, 313 MeV. The same mechanism that produces the mass of leptons should produce this mass,

Koide rule is that the mass of leptons is

313.188449 MeV ( 1 + sqrt(2) cos(phase))^2

The square is also inspiring, it seems as if the interesting quantity is actuall sqrt(mass).

The constituent quark mass scale is still the same (to within 5-10%) even in what Frank Wilczek calls "QCD Lite" - just two quark flavors with no current mass. So undoubtedly this mass scale is produced within QCD. So far I don't have a simple explanation for its value; we can only hope that there's some simpler way to get it, other than long lattice calculations.

Assuming the connection between the constituent quark mass scale and the Koide relation scale factor is real, it is surely being produced within QCD and transmitted to the leptons. And consider this: simple algebraic transformations of the formula above can bring a factor of 2 out of the squared term, so now we have "mass(lepton) = 2 . mass(constit.quark.) . (new squared term)". In your correspondence, the leptons pair supersymmetrically with mesons, i.e. a quark and an antiquark. So the "naive meson mass", assuming the u/d constituent quark mass scale, is of the order of 2 x 313 MeV.

In other words, one can imagine a sort of "Rivero-correspondence Standard Model Lite", in which all flavors of quark have zero current mass, in which they take on the 313 MeV constituent mass (because of QCD effects) in mesons and baryons, and in which the 625 MeV "naive meson mass scale" gets transmitted to the lepton "superpartners" of the mesons. If such a field theory existed, we could then think about modifying it so that the quarks have nonzero current masses, and so that the charged lepton masses are altered by the extra factor appearing in the Koide formula above.

 

[qsa]

The constituent quark mass scale...

here is the chart I promised you.

 

[mitchell porter]

Something which has previously bothered me is that, if you were trying to make a "quark-diquark superfield" or a "lepton-meson superfield" - that is, if you were trying to apply the standard superfield formalism to this idea - it shouldn't make sense, because the two "components" (at least, in the quark-diquark case) aren't independent degrees of freedom.

But I wonder if you can get around this by just pretending that they are independent, and later imposing a quantum constraint? In fact, I wonder if this could be done to the MSSM? Until this point, I thought there were only two ways to realize this correspondence in terms of the MSSM: Either you have the MSSM emerging from something like SQCD, or you have an extra emergent supersymmetry within the already-supersymmetric MSSM. The reason is, once again, that quarks and squarks are independent degrees of freedom in the MSSM, but quarks and diquarks are not. So either quark-diquark supersymmetry is an emergent extra supersymmetry, in addition to quark-squark supersymmetry, or else the squarks are really the diquarks of a simpler, SQCD-like underlying theory. The idea of a "quantum constrained MSSM" - not to be confused with the parameter-constrained MSSM that is usually denoted by CMSSM; I mean a constraint whereby we project out part of the Hilbert space - would have to be a version of the latter possibility.

But the idea of quark-diquark supersymmetry emerging within the MSSM is curious. On the one hand, it seems like it ought to be well-founded, because QCD does unquestionably exhibit an emergent approximate quark-diquark supersymmetry - this is where the idea of hadronic supersymmetry came from. But adding another supersymmetry to the N=1 supersymmetry of the MSSM should produce N=2 supersymmetry - shouldn't it? - and N=2 theories can't be chiral. This seems like a question of authentic theoretical interest, independent of phenomenology: What happens when you examine hadronic supersymmetry in the context of the MSSM? Does it just break down because of the extra states?

edit: This is not exactly the same thing, but wow: Two papers on finding a Seiberg dual for the MSSM! (http://arxiv.org/abs/0809.5262" ). Possibly in the context of a dual for susy SU(5) GUT. That is, you'd find a dual theory for susy-SU(5), and I guess you'd also find a dual description for breaking it down to MSSM.

The MSSM is criticized for having 120 parameters, but http://golem.ph.utexas.edu/~distler/blog/archives/000681.html" , most possible values of those parameters will probably prove to be unrealizable. So one might hope for a unique mechanism explaining the deformation away from exact supersymmetry (in which e.g. lepton masses would equal diquark masses, see comment #58) which may underlie the Koide formula.

edit #2: For the exactly supersymmetric form of the MSSM, reduced to a single line, see page 95 (equation 465) of http://arxiv.org/abs/hep-ph/0505105" .

 

[arivero]

For the exactly supersymmetric form of the MSSM, reduced to a single line, see page 95 (equation 465) of hep-ph/0505105.

I bought the book!

 

[arivero]

I just read the last confrontation between Motl and Woit... It is not worthwhile to try to comment on this at either blog (Woit actually censurates me and Motl allows posting but well, surely he just prefers to make fun of people instead of actually censurating, at least in my case). But it is worthwhile to read them, specially if you have in mind the perspective of the "wrong turn"... and that we know that the argument about the purity of hep-th fails, because it is almost impossible to find papers with an unbroken or midly unbroken susy, and well, Mitchell has practically revised all the arxiv for papers useful here, and only got a handful of them.

 

[arivero]

After all this LHC excitation, I am afraid i could go into hibernation for some period, but I want to say some words about this 313 GeV thing and how, to my regret, it could relate to extra dimensions. The point is that if we want quarks and leptons to stand in some symmetry group, the smaller candidate is SU(4), "Lepton number as the fourth color". The full group Pati Salam thing, SU(4)xSU(2)xS(2), is known to appear with 8 extra dimensions: it is the group of isometries of the manifold S5xS3, the product of the three-sphere with the five-sphere. It was argued by Bailin and Love that 8 extra dimensions are needed to get the charge assignmens of the standard model, but I am not sure if this manifold was used. Its role was stressed by Witten, who pointed out that the family of 7-dimensional manifolds that you get by quotienting this one via an U(1) action have the isometry group SU(3)xSU(2)xU(1).

I liked to think of this compactification as an infinitesimal extra dimension, partly because of the hint of F-theory, partly because thile the SU(4) group seems a need, I don't like to look at it as a local gauge group.

Again, this was well known lore of supergravity (and even in string theory) in the early eighties, but in the same way that the first revolution wiped gluons away, the second string revolution killed the research on realistic Kaluza Klein theories.

 

[mitchell porter]

I made a https://www.physicsforums.com/showthread.php?p=3423211" for this 12-dimensional idea.

edit: Meanwhile I observe that we can get SO(10) (which contains http://math.ucr.edu/~huerta/guts/guts.html" .

 

[mitchell porter]

With the modern ideas (strings, branes, strings between branes, strings/branes wrapped around noncontractible submanifolds...), you can get Pati-Salam in other ways too. Maybe the boldest neo-Kaluza-Klein hypothesis would be to say that all of these modern possibilities arise from dualities applied to a very-high-dimensional theory that is pure Kaluza-Klein. E.g. T-duality can take a space-filling brane and turn it into a brane of codimension one. But that discussion belongs in the other thread.

In order to relate quark-antiquark and lepton supersymmetrically, I have also been looking at another idea from the Time Before Arxiv: supersymmetric preon theories. This is because it is quite difficult to get elementary and composite fields into the same supermultiplet. I know of one example of http://arxiv.org/abs/hep-th/0207232" , but all the components of the supermultiplet are composite. So it might be easier to have quarks and leptons already composite. There is a big literature on supersymmetric preon models, again from the 1980s. I won't list individual papers, but reviews by Volkas look useful.

A more concrete form of guidance, complementary to the Koide formula, is the fact that the pion mass is about the square root of the constituent quark mass. (I believe this has a derivation in terms of chiral perturbation theory, and also a holographic derivation.) The way I think about this is as follows. Suppose we consider the hypothetical "exactly supersymmetric" realization of the correspondence, in which particles and their superpartners are the same mass. So a lepton is trying to be the same mass as a meson, which has two constituent quarks, implying a natural mass scale of 626 GeV - and as I pointed out, you can rewrite the Koide formula so it's 626 GeV multipled by a phase-dependent factor (thanks to basic trigonometric identities). But at the same time, a quark is trying to be the same mass as a diquark - and here we get a direct contradiction, or a tension that has to be resolved. I'm thinking that this pion mass relation is a clue to how the tug-of-war on that side is resolved, even though a pion should supposedly pair up with a lepton. (I suspect the basic relations are actually between "operators" or "currents", e.g. that there's a relation between a quark current and a diquark current, and that the properties of the physical particles, like pion, eta meson, kaon, only exhibit an echo of the basic relations.)

I also found work on the idea that http://www.sciencedirect.com/science/article/pii/0550321384902608" , which dates back to a paper by Weinberg, and which has contemporary correlates in string theory. This is what the reference to "technicolor instantons" in comment #55 was about; the idea is that the nucleons get their mass from QCD instantons, so if the Koide mass scale of the leptons is the same thing, there should be a picture in which the leptons are also getting their mass that way.

 

[arivero]

A new thread can be a good thing.

13 dimensions? Yep I noticed it was needed for SO(10) -and I will not ask for manifolds whose isometry group is E6,E7 or E8- and I was very afraid of this overplus of dimensions. :-(

Perhaps the rule that limits the max dimension to 11 applies only to the production of the gauge group. IE, we can put more dimensions but in order to produce a gauge group we are limited, from some consistency rule somewhere, to choose eleven of them.

 

[qsa]

A more concrete form of guidance, complementary to the Koide formula, is the fact that the pion mass is about the square root of the constituent quark mass. (I believe this has a derivation in terms of chiral perturbation theory, and also a holographic derivation.) The way I think about this is as follows. Suppose we consider the hypothetical "exactly supersymmetric" realization of the correspondence, in which particles and their superpartners are the same mass. So a lepton is trying to be the same mass as a meson, which has two constituent quarks, implying a natural mass scale of 626 GeV - and as I pointed out, you can rewrite the Koide formula so it's 626 GeV multipled by a phase-dependent factor (thanks to basic trigonometric identities). But at the same time, a quark is trying to be the same mass as a diquark - and here we get a direct contradiction, or a tension that has to be resolved. I'm thinking that this pion mass relation is a clue to how the tug-of-war on that side is resolved, even though a pion should supposedly pair up with a lepton. (I suspect the basic relations are actually between "operators" or "currents", e.g. that there's a relation between a quark current and a diquark current, and that the properties of the physical particles, like pion, eta meson, kaon, only exhibit an echo of the basic relations.)

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my idea strongly suggests that the above line is the more correct one. if you have one particle its energy is tiny (inverse of the size of the universe) and nothing interesting happens. but as soon as you have two of them then you get all the fireworks like you see in the attachment. but that is done for a small universe, for a bigger universe and more resolution you get more complicated shape in the running phase but always stablazing somewhere about 3* electron compton(those formulas I showed you seem to be related to this). and at distances on the order of bohr radius then I get exactly the hydrogen numbers, energy and all. so, just like the hydogen when the KE and PE have some relation for stable system ,it seem you also have that at shorter distances. i am working on that now. I will PM you soon the details.

 

[qsa]

this is the most beautiful chart ever. no matter what compton(172,182,364,1000) you always end up at interaction distance of 5468 with the energy of .00054858 . that is what is so special about the mass of the electron.

 

[mitchell porter]

I was looking at notes from http://pyweb.swan.ac.uk/~pyarmoni/oberwolz.pdf" , and nearly fell over when something extremely simple jumped out at me. See pages 25 and 26. He's talking about work by Sagnotti on "Type 0 string theory". Apparently it offers a realization of hadronic supersymmetry in which a meson is a bosonic oriented string connecting a quark and an antiquark, and a baryon is a fermionic unoriented string connecting a quark and a quark; there is some sort of fermionic field along the length of the string.

So then it hit me: could such a model then incorporate a diquark as a bosonic oriented string connecting a quark and a quark? And what about its "partner", an unoriented string connecting a quark and an antiquark, with a fermionic field running between them?

Would that offer a way to place the leptons in a Type 0 string theory, in a way that extends hadronic supersymmetry?!

Having stated the very attractive idea, now let me state a few problems. First, it's unclear to what extent this model of open strings can possibly reproduce all the observed complexities of hadronic physics. Also, we don't see free diquarks in reality. But then, maybe we don't have to; what we need is a "fermionic quark-antiquark" that is stable and is actually a lepton. It's OK if a free "diquark string" is unstable.

http://arxiv.org/abs/0901.4508" goes into further stringy technicalities.

 

[mitchell porter]

My remarks were a little confused. But it's one of the confusing things about Alejandro's correspondence.

In theory, hadronic supersymmetry relates an antiquark and a diquark (quark-quark pair). In practice, what we see are similarities between a meson (quark-antiquark) and a baryon (quark-diquark). To obtain the baryon from the meson, we substitute the diquark for the antiquark.

Alejandro's extension of hadronic supersymmetry relates a lepton to a quark-antiquark pair. Unlike hadronic supersymmetry, there's no known dynamical significance to this correspondence (but this is why we are talking about the similarity between the constituent quark mass scale and the mass scale appearing in the Koide relation). It's just that the electromagnetic charges match up; by pairing quarks with antiquarks, you can make composites with charge -1, 0, and +1, which matches the charges one sees in the elementary leptons, "as if" they were superpartners to these quark-antiquark combinations.

The combination of quark and antiquark is normally a meson. But we see that for quark-diquark symmetry, we can't speak of it as true in all imaginable contexts. For example, I don't think you can "substitute a diquark for a quark" in any meaningful way, if the quark is already part of a diquark. Indeed, hadronic supersymmetry is usually said to be an emergent symmetry, true because diquarks resemble quarks under certain circumstances (as substructures of a hadron), not because the fundamental theory is supersymmetric. It's only a very rare theorist like Sultan Catto who is trying to explain hadronic supersymmetry as a manifestation of a fundamental supersymmetry.

So the posited relationship between "mesons" and leptons is even more tenuous. As I said a few comments back, I suspect that if such a relation exists, it's fundamentally algebraic, and may be obscured to the point of invisibility in the actual mesons. Furthermore, the observable mesons already play a role in quark-diquark symmetry - you can substitute a diquark for one of their constituent quarks, and get a baryon with similar properties.

This was the genesis of my confusion about Armoni's talk. The "orientifold field theories", which arise from certain models in Type 0 string theory, exhibit a supersymmetry between a bosonic "meson" string and a fermionic "baryon" string. The meson-baryon relationship exists in hadronic supersymmetry, so I jumped to the conclusion that if we changed the sign of one of the quarks terminating these Type 0 strings, we could implement Alejandro's idea.

But in fact, Alejandro's idea applies directly to "mesons", i.e. to quark-antiquark strings, such as exist in "orientifold planar equivalence". So really, the more logical way to employ planar equivalence here would be to say that its "meson-baryon supersymmetry" actually corresponds to Alejandro's "meson-lepton supersymmetry"; and then we should seek to extend planar equivalence so as to include bosonic "diquark strings" which will be dual to fermionic "quark strings". This last step sounds problematic, to put it mildly. Maybe there's some other way to proceed. But I had to make this clarification.