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

[mitchell porter]

I also want to make some remarks about hadrons from the perspective of contemporary string theory.

Consider a stringy standard model such as appears in Barton Zwiebach's textbook. Other string models work differently to this, but this one allows me to make my point. There are several intersecting stacks of D-branes, and all the fundamental particles are open strings running between the brane stacks. There is a stack of 3 branes, one for each color in QCD. Strings between these branes are the gluons. There are also separate stacks of "left branes" and "right branes". Quarks are strings that connect a color brane with a left brane or a right brane. (There are also lepton branes, and leptons are strings connecting lepton branes with a left brane or a right brane.) Having left branes and right branes, and thus different strings for left-handed and right-handed quarks, is a way to have them behave differently, as in the real world.

Now consider what a hadron is. It's a bunch of quarks, bound together by the exchange of gluons. In the string model above, gluons are strings interior to the stack of color branes, and quarks are strings stretching from the color branes to the "handedness" branes. A hadron, therefore, is a "bundle" of two or three (or more) "quark strings", stretching between color branes and handedness branes, exchanging a lot of "gluon strings" at the color-brane end of the "bundle". A very approximate image might be a bouquet of flowers; each flower is a quark, the petals are at the "left brane" or "right brane", and the stems stretch down to the color branes - and that's where the bouquet is tied together, by the gluons. The important part of this image is the idea that a hadron is a bundle of quark strings, tied together at the color end.

This is a rather more complex model of a hadron than in the Type 0 string model discussed by Armoni. There, a meson is a single string, connecting two "quark branes", and not a bundle of two strings, connecting two separate brane stacks. This is more akin to the way mesons were described in the "dual resonance models" which ultimately gave rise to string theory.

This has big implications for how one might seek to realize hadronic supersymmetry, and its generalization to leptons, within string theory. The strings in the model from Zwiebach's textbook are superstrings, so at the particle level they correspond to superfields. That is, the "quark strings" that I mentioned, actually describe quarks and squarks. It's only when supersymmetry is broken that the bosonic and fermionic aspects of the string acquire different masses, and all those different classes of string become identifiable, at low energies, with just one or the other.

I haven't really studied Type 0 string theory yet, but although it's technically not supersymmetric, I get the impression that a sort of residual supersymmetry exists, and that the "meson-baryon supersymmetry" discussed by Armoni is pretty much the same thing as the coexistence of boson and fermion within a single string in ordinary supersymmetric string theory. The "baryon" is just the fermionic counterpart of the "meson" string.

But if we consider the "bundle" model of hadrons that arises in conventional string phenomenology, it's clear that the superpartner of the bundle is a much more complicated entity - that is, if it can be said to exist at all.

The bottom line is that the implementation of hadronic supersymmetry, and hence of its extension to the leptons, is potentially much more economical in Type 0 string theory than in conventional string phenomenology, because mesons and baryons could themselves be fundamental strings, and not "bundles" of fundamental strings. That perspective is part of what was abandoned by the "turn" of string theory mentioned in the title of this thread.

 

[arivero]

Still, I remember I visited works similar to Armoni's time ago. An idea was to get leptons via transitions between hadronic states, but lepton and baryon numbers get involved and block the way. Another was to think that this "1/2 spin in the string" of some models of baryons was to be interpreted not a a third quark, but as the superpartner, string-wise, of the spin 1 gluon. But then one needs to explain how two spin 1/2 particles get to exchange another spin 1/2 particle: fields must be always bosonics. On the other hand, just this problem could explain why the leptons are points: a spin 1/2 open string should always be a point, because only boson fields can be extended in space.

Sagnotti seems always to be near of something, but then he jumps elsewhere. I was very excited with his work with Marcus, where he got the SO(32) group as a consequence of open strings in the worldsheet, before the advent of the tadpole interpretation.

 

[mitchell porter]

A few times I remarked on the fact that work on GUTs didn't concern itself with mesons and baryons. So it's fascinating to see that "holographic QCD" does. In fact, I think the pursuit of holographic QCD within Type 0 string theory offers the best opportunity yet to realize your super-bootstrap.

Standard holographic QCD works in Type II string theory. You have a stack of flavor branes intersecting a stack of color branes; quarks, gluons, and mesons are various open strings between the branes; and baryons are localized branes connected by strings to the color and flavor branes. By the way, this is "top-down" holographic QCD, where you use the full string theory. AdS/QCD usually means "bottom-up" holographic QCD, where you define a five-dimensional AdS geometry but don't necessarily have an embedding into string theory.

Fantastic progress has been made in realizing phenomena of QCD like chiral symmetry breaking and confinement, and in getting predictions for meson and baryon masses, but there still isn't a canonical holographic model of QCD - the top-down constructions are all supersymmetric. Also, one of the frontier problems for holographic QCD is to model the diquark condensate which breaks chiral symmetry in the "color-flavor locking" phase of "three-flavor QCD" (three light flavors, that is). There doesn't seem to be a standard representation of diquarks yet (they feature in some of the bottom-up, AdS/QCD work, but I think more as a numerical factor than a geometric object); though I have run across http://arxiv.org/abs/1101.1120" . The flavor branes are D8-branes (if you work within Type IIA string theory), and the proposal is that the diquark-diquark string is a D6-brane connecting the two flavor branes involved in the diquark condensate, with five of its dimensions compactified on the S^5 factor of the AdS geometry - leaving just one worldvolume dimension uncompactified, so it looks like a string.

http://arxiv.org/abs/0902.4515" "This D4-D8 model was slowly developed over the years, starting with Witten’s initial identification of the dual geometry for D4 branes wrapped on a thermal circle, study of glueball mass spectra of pure QCD without matter, the introduction of mesons via D8 branes, and very recent study of baryons as solitonic objects on D8 branes." The fact that here, quarks are strings, mesons are strings, and there may even be a diquark-diquark "string", should make us very optimistic that hadronic supersymmetry could become a real supersymmetry here, and that it might be extended to include the leptons.

Now let us return to the Type 0 string. This is a nonsupersymmetric string theory, essentially discovered by Sagnotti, which can be obtained from M-theory by an unusual quotient. Everything works a little differently - for example, instead of just having D-branes distinguished by their dimension, the D-branes have the extra property of being "electric" or "magnetic" - but you can do http://arxiv.org/abs/hep-th/0202024" . At least, up to a point. I think the main reason there has been so little work is because the lack of supersymmetry makes it hard to calculate. Nonetheless, there's an echo of supersymmetry, e.g. in the Bose-Fermi mass degeneracy between bosonic and fermionic strings explored by Armoni and Patella. In fact, that echo is potentially all we need to realize the super-bootstrap. Quark-diquark supersymmetry is not dynamical, in the sense of there being gauginos, nor is its extension to the leptons. At this stage, I wouldn't advise to completely forget about the MSSM and related possibilities, but it seems obvious that the Type 0 string has just enough "sub-supersymmetry" to explain all the facts. All that's needed - and this is still not easy! - is to find a Type 0 realization of QCD and the Standard Model with the indicated features.

 

[arivero]

... ... is to find a Type 0 realization of QCD and the Standard Model with the indicated features.

A puzzle, or a hint, is the need of doing QCD, not SU(N). The diquark depends essentially of SU(3) colour, so I am a bit suspicious of any AdS/CFT when they need to have some limit for big N.

And then, the same goes for any attempt to do the trick with strings a la Sagnotti. In 4D space time, SU(3), or even SU(3) colour times U(1) electromagnetic, should appear.

 

[mitchell porter]

How is http://blog.vixra.org/2011/08/13/has-the-lhc-seen-the-higgs-boson-at-144-gev/#comment-9775" which posits that both Higgs and top are composites, and claims to get the Higgs values currently under consideration at vixra.) Leptons as mesinos - I can imagine that working - but it becomes a little paradoxical to say that quarks are fermion-string "diquarkinos", at least when you talk about the quarks other than the top, because they are also supposed to be what terminates the strings. That would be the most involuted part of the bootstrap, and I can't quite see how to do it.

edit: Some interconnected observations.

First, let's consider one simple way the superbootstrap might work. We have a few fundamental quarks and antiquarks, they can be held together in bosonic composites by gauge bosons (e.g. gluons), and we can also form fermionic composites in which the gauginos are the intermediate operator. These three-object combinations might be thought of as http://physics.stackexchange.com/questions/13101/is-there-a-sqcd-gluino-string-similar-to-the-gluon-string" - quarks and/or antiquarks at the ends, gaugeons and gauginos along the string - or more neutrally, they might be thought of as ordered products of three field operators.

So, we have quarks and antiquarks. We have quark-quark and quark-antiquark pairings, which we call diquarks and mesons respectively, which have boson statistics, and which are implicitly "quark-gaugeon-quark" and "quark-gaugeon-antiquark". Finally, we have superpartners of these, which take the form "quark-gaugino-quark" and "quark-gaugino-antiquark", and which have fermionic statistics.

The super-bootstrap, interpreted in this framework, says that the leptons are actually "quark-gaugino-antiquarks", i.e. mesinos. OK, it remains to be demonstrated that this is viable, but there's no overt paradox so far. But the other part of the scheme, inherited from hadronic supersymmetry, is that quarks themselves are "quark-gaugino-quarks" - a quark is a "diquarkino". This is paradoxical because of its recursion. The numerology of the scheme assumes that u,c,d,s,b are fundamental, so there's no paradox for the top; but how are we to understand the mutual compositeness of the other five quarks? Can you "substitute" one diquarkino into another diquarkino? Or can the recursive relations posited to connect the quarks be realized in terms of further, non-recursive, fundamental compositeness? (i.e. preons)

The other factor I have to mention here is the role of http://physics.stackexchange.com/questions/5232/what-restricts-the-value-of-weak-hypercharge-from-being-5-3" . This could certainly cause problems for the scheme, but I also wonder if you couldn't try to tie those values of 4/3 to the problematic uu, uc, cc pairings.

 

[MTd2]

How do we know that the top quark is actually a quark? It has no time to form a bound stat e so it actually displays a non confined color. How do we know it is not something else?

 

[arivero]

How do we know that the top quark is actually a quark? It has no time to form a bound stat e so it actually displays a non confined color. How do we know it is not something else?

't Hooft, anomalies.

And speaking of 't Hoft, we also guess that there is something more, if we use the naturalness principle; in some limit where the mass of the top is, say, 1, and all the other are zero, a symmetry should cover all the other fermions except the top. Time ago I was intrigued because "all the other fermions" means 84 helicities, a pretty number.

 

[arivero]

The other factor I have to mention here is the role of http://physics.stackexchange.com/questions/5232/what-restricts-the-value-of-weak-hypercharge-from-being-5-3" . This could certainly cause problems for the scheme, but I also wonder if you couldn't try to tie those values of 4/3 to the problematic uu, uc, cc pairings.

Yes! The guiding principle should be that while the uc and dd pairs can be organised in three generations of Dirac supermultiplets, the uu only can do three generations of purely chiral supermultiplets. So uc and dd types are able to "see" the vector charges, colour SU(3) and electromagnetic U(1), but uu type can not. So they (the uu type combinations) should be considered "neutral", with no tree level coupling to the gluons, from the point of view of SU(3), even if they are the combination of two charged objects... And even something more strange with photons, I have not worked it out.

 

[MTd2]

't Hooft, anomalies.

What I mean is the Top being something other than a quark. That is, a top is a quark and also something else.

 

[mitchell porter]

What I mean is the Top being something other than a quark. That is, a top is a quark and also something else.

That's an interesting idea. See http://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-to-look-for-supersymmetry-at-the-lhc/" ... in the MSSM, there are all those other heavy particles; how would you know that the phenomenological top isn't really a top plus a squark, for example?

The top has been heavily studied at the Tevatron, I imagine there would be answers to this question somewhere in the literature.

edit: http://www.phy.bnl.gov/~partsem/fy09/TTait_Talk_06_19_09.pdf" says the best opportunities for something more than pure top to show up, is in the vertex for four right-handed tops.

 

[mitchell porter]

Yes! The guiding principle should be that while the uc and dd pairs can be organised in three generations of Dirac supermultiplets, the uu only can do three generations of purely chiral supermultiplets. So uc and dd types are able to "see" the vector charges, colour SU(3) and electromagnetic U(1), but uu type can not. So they (the uu type combinations) should be considered "neutral", with no tree level coupling to the gluons, from the point of view of SU(3), even if they are the combination of two charged objects... And even something more strange with photons, I have not worked it out.

I guess you mean "ud and dd", not uc?

Also, a "Dirac supermultiplet" is a type of supermultiplet peculiar to AdS space, made of a pair of "singleton" representations which only live on the boundary. It was the subject of a paper by Fronsdal, and Michael Duff even employed in a bootstrap conjecture (see "Supermembranes: the first fifteen weeks"). But I assume you just mean a vector supermultiplet containing Dirac fermions?

 

[mitchell porter]

For reference, I'll link to some earlier discussions: https://www.physicsforums.com/showthread.php?t=457825&page=8#114".

This idea of placing gauge bosons in vector supermultiplets creates another problem/clue for the sbootstrap. The problem is that gauginos transform in the adjoint representation of the gauge group, but Standard Model quarks are in the fundamental representation. The clue: as Armoni and Patella note, for SU(3), and for "two-index" representations, the adjoint representation and the antisymmetric representation are the same. Two-index representations are appropriate for products of two quark operators, such as diquarks or mesons.

I see two ways to go about utilizing this fact. One way is to focus just on color SU(3), the other would be to look at getting the weak interaction from flavor SU(3)^n, n>=1.

edit: If we go to http://physics.stackexchange.com/questions/13629/gut-that-includes-all-3-particle-families-into-a-large-group" .

 

[mitchell porter]

And speaking of 't Hoft, we also guess that there is something more, if we use the naturalness principle; in some limit where the mass of the top is, say, 1, and all the other are zero, a symmetry should cover all the other fermions except the top. Time ago I was intrigued because "all the other fermions" means 84 helicities, a pretty number.

I like this number because it's half of 168, the number of symmetries of the Fano plane i.e. the unit octonions. I should also link back to our https://www.physicsforums.com/showthread.php?t=447612".

At one level, my model of how to think about sbootstrap has been (super)QCD with five massless quarks and one massive quark, the top. But if we consider the posited quark/diquarkino identity, then it seems like the five 'massless' quarks are fundamental and the top is just one among many (super)composites. What could make it special? Well, here I think of http://motls.blogspot.com/2008/12/ckm-matrix-from-f-theory.html" , which as I recall amounts to showing that a generic sort of geometry will produce a preferred direction in CKM matrix space. Perhaps one could do the same for the top. In other words, it's not that there is something special about the top, but rather, there will inevitably be a heavier quark, and the top happens to be it. Though one might still want to know why it's a +2/3 rather than a -1/3.

Anyway, the idea is that then, the other 84 degrees of freedom possesses a residual symmetry, resulting from "dividing out" by the top in a larger symmetry. And the 168-element symmetry group of the Fano plane, http://en.wikipedia.org/wiki/PSL%282,7%29" . (In the literature, it's often called "Delta(168)".)

 

[arivero]

I guess you mean "ud and dd", not uc?

Also, a "Dirac supermultiplet" is a type of supermultiplet peculiar to AdS space, made of a pair of "singleton" representations which only live on the boundary. It was the subject of a paper by Fronsdal, and Michael Duff even employed in a bootstrap conjecture (see "Supermembranes: the first fifteen weeks"). But I assume you just mean a vector supermultiplet containing Dirac fermions?

Yes to both... I am very sloopy, you see But yep, it is "ud and dd", and it is just a supermultiplet (this should be more generic that vector, even if in this case is a massive vector one) containing Dirac fermions.

 

[MTd2]

That's an interesting idea. See http://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-to-look-for-supersymmetry-at-the-lhc/" ... in the MSSM, there are all those other heavy particles; how would you know that the phenomenological top isn't really a top plus a squark, for example?

I was not really thinking about the compositeness of the top quark. I was thinking if the top quark could be something else like a 4th generation lepton besides being also a quark.

 

[arivero]

I was not really thinking about the compositeness of the top quark. I was thinking if the top quark could be something else like a 4th generation lepton besides being also a quark.

I still don't get it. Do you mean the *signal* of the top in accelerators, to be really a mix of two signals? Surely this is mostly ruled out by secondary observables.

 

[MTd2]

Not a signal. I am brainstorming here about the nature of the top quark. It doesn't have a half life long enough to hydronize. But colors are confined, so a top quark must be bound to an anti color gluon, right?

 

[mitchell porter]

Every hadronization event (jet) starts with a quasi-free quark. But the top changes flavor before hadronization can occur. So this issue isn't specific to the top.

I can see two ways to think about it. Jets don't occur in isolation; top quarks are always produced along with other (anti)quarks. So it could be that, even though these quasi-free quarks - parents of the jets - aren't bound to each other, their total wavefunction may be color-neutral.

Alternatively, it may just be a matter of scale (length and time). Confinement - of color, of quarks - sets in somewhere above 10^-15 m. The top quark decays in 10^-25 s. Maybe it just doesn't live long enough for confining dynamics to matter.

Just from skimming the literature, I can't see that one concept or the other is favored. But then I cannot see a rigorous dynamical explanation of hadronization in the literature, just various rival models. There may be something of a "plasma of models" here. :-)

 

[MTd2]

Every hadronization event (jet) starts with a quasi-free quark.

What do you mean by quasi-free?

 

[mitchell porter]

What do you mean by quasi-free?

I just mean, not currently part of a hadron. How that works depends on the model of hadronization. The Lund model (http://arxiv.org/abs/hep-ph/0212122" ) provides a useful example because of its simplicity. In the Lund model, you have a string that stretches and breaks into a sort of discretized spacelike hyperbola, the elements of which are the outgoing hadrons. Now consider a point in the history of one of the quarks terminating the original string, when it is far away from its partner but before the fragmentation which creates the outgoing hadron to which it belongs. At this time, when the quark is between hadrons, it's not exactly free, but it isn't confined either.

edit: The Lund model is just something I came across while answering your question, but it turns out to have a http://arxiv.org/abs/1007.4313" ! This is very cool because it's a QCD string model, containing diquarks, that is used to describe the difficult dynamics of hadronization. It's great to have a potential bridge between Alejandro's correspondence and something as concrete as a scattering process.

 

[mitchell porter]

After staring at the http://math.ucr.edu/~huerta/guts/node11.html" assignments for a while, I have devised a new approach to this whole idea. I haven't even tried to get the right numbers of particles, I just want to mention it as a mutant form of the hypothesis which might assist its analysis.

Alejandro's idea involves pairing (anti)quarks, adding the electric charges, and then supposing that these pairings have superpartners, and is called the super-bootstrap. I do the same, except that I add the ordered pairs (weak hypercharge, weak isospin), so I call it the "hyper-bootstrap".

To add ordered pairs, the rule is (a0,b0)+(a1,b1)=(a0+a1,b0+b1). There is also a secondary "rule" that you can add two ordered pairs which both have nonzero weak isospin, only if one has isospin +1/2 and the other has isospin -1/2. Also, you only add quarks; leptons are an exit point. (This is "because" only quarks feel color, and the strong force is the rationale for all the pairings.) And finally, you only add two ordered pairs at a time.

To begin with, we suppose we only have left-handed quarks and right-handed antiquarks to work with; so we have ordered pairs of the form (+/- 1/3, +/- 1/2). Because of the secondary rule about only adding nonzero isospins of opposite signs, the only ordered pairs we can make from these are (0,0) and (+/- 2/3, 0). That is, left-handed neutrino / right-handed antineutrino, and left-handed down-type antiquark / right-handed down-type quark.

Next, suppose we are adding ordered pairs of the form (+/- 2/3, 0). From this we can again get (0,0), and we can also now get (+/- 4/3, 0), i.e. right-handed up-type quark / left-handed up-type antiquark.

Next, suppose we are adding ordered pairs (+/- 2/3, 0) and (+/- 4/3, 0). This allows us to get (+/- 2/3, 0) and (+/- 2, 0). So here the hyper-bootstrap offers an additional way to obtain (+/- 2/3, 0), as well as putting right-handed electrons / left-handed positrons (and their muon and tauon counterparts) within reach.

Finally, suppose we add (+/- 1/3, +/- 1/2) and (+/- 2/3, 0). This allows us to obtain (+/- 1, +/- 1/2) ... left-handed leptons and right-handed antileptons ... and (+/- 1/3, +/- 1/2) ... left-handed quarks and right-handed antiquarks again, the hyper-bootstrap feeding into itself again.

As happens for Alejandro, I don't have a rule that prevents me from combining (+/- 4/3, 0) with itself, so I also get the annoying extra combination (+/- 8/3, 0). edit: Nor do I have a rule against adding (+/- 4/3, 0) with (+/- 1/3, +/- 1/2), which produces (+/- 1, +/- 1/2) as above, and another nonexistent assignment (+/- 5/3, +/- 1/2).

Obviously the hyper-bootstrap and the super-bootstrap have considerable similarities - including the leftover at the end! And we need to examine whether the actual multiplicities, of quark fields and their combinations, work at all. But it's interesting that even at the slightly finer-grained level which considers isospin and hypercharge quantum numbers separately, you can still define a similar scheme.

 

[mitchell porter]

A sketch is attached.

 

[arivero]

There is also a secondary "rule" that you can add two ordered pairs which both have nonzero weak isospin, only if one has isospin +1/2 and the other has isospin -1/2.

It seems reasonable, as then we can look for some symmetrization argument to justify the idea. But is is also peculiar. It means that the uu and dd combinations only happen for R type quarks.

Looking at the reference of Huerta, I note that in http://math.ucr.edu/~huerta/guts/node10.html the previous section he takes some pains to discuss the adjoint representation of U(1) and its role in the hypercharge. A subltle point here is that U(1)-hypercharge is still chiral (as Distler likes to stress) and then it needs complex representations, while U(1) electromagnetism is not.

 

[mitchell porter]

I've counted up the combinations, see attachment.

As input, I've taken every ordered pair (weak hypercharge, weak isospin) that is actually realized by a quark in the standard model. In the table I list every possible summation of two such ordered pairs (I have dropped the "secondary rule" which excluded outcomes with a "weak isospin of +/- 1"). Finally, I calculate multiplicities (represented in the table by subscripts) by assuming that I'm just working with udscb.

For example, in adding (-1/3,1/2) and (1/3,-1/2) to get (0,0), there are nine combinations, because the inputs correspond to an electric charge of magnitude 1/3, so there are three flavor options for each. Whereas, in adding (1/3,1/2) and (2/3,0) to get (1,1/2), we are adding an electric charge of magnitude 2/3 to an electric charge of magnitude 1/3, so (by the rules of the game) we have two flavor options for the first (no top) and three flavor options for the second. Everywhere in the table, to get the multiplicity, I just multiply two numbers in this fashion, except along the diagonal, where we are pairing elements of the same set. So three flavors gives six possibilities (dd ss bb ds sb bd), two flavors gives three possibilities (uu uc cc).

Each ingredient of each combination is specified by a handedness, a flavor, and whether it's a quark or an antiquark. So we are talking about pairings of the form "left-handed bottom antiquark + right-handed charm quark".

In making sense of the resulting table, I have excluded from consideration (for now) any combination of isospin/hypercharge quantum numbers which does not correspond to a standard model particle. These are labeled "exotics" and crossed out. We are therefore left with an enumeration of "how many ways to reproduce the weak quantum numbers of any standard model fermion, by pairing quarks other than the top".

For the quarks, for all but two outcomes, there are six ways to do it. What we really want is three (the number of generations), but perhaps we can think of pairing the six off in superposition. For (1/3,1/2) and (-1/3,-1/2), there are nine options, as if we want three elements in superposition per flavor, rather than two. Curiously, these are states with electric charge of magnitude 2/3, so maybe we should group them into superpositions with two, two, and five elements, with the five-part superposition being the top.

For the leptons, characteristically there are 12 (6+6) or 13 (4+9) ways to obtain any given outcome. The exceptions are (+/-2,0), but these can be paired up with half the (0,0)s - we have 26 of those. Anyway, here it seems we want four elements in a superposition corresponding to a single standard model species of fermion (specified at the flavor, handedness, (anti)particle level), rather than two.

And then there are all the exotics, the pairings that don't obviously correspond to anything. Some of these have the electric charge of a quark, but the hypercharge and isospin are wrong.

 

[mitchell porter]

You could say that this "hyper-bootstrap" is the super-bootstrap at four times the resolution. Where previously we just combined quarks and antiquarks (e.g. as described https://www.physicsforums.com/showthread.php?t=457825&page=8#127".

As a statement about actual physics, my tabulation of combinations is about as naive as it could get without being completely irrelevant to the real world. All the inputs, at least, are real. Unrestricted combination of left quarks and right quarks is probably wrong, but we do have to take chirality into account eventually, since left and right have different electroweak quantum numbers. I also haven't taken any representation theory into account. If someone just told you that gluons have the form "color-anticolor", where color is RGB, you would assume that there were 9 gluons, but in fact there's only 8. The multiplicities in my table may be reduced or altered by similar considerations. Also, we know that the actual QCD spectrum is http://physics.stackexchange.com/questions/13458/what-the-heck-is-the-sigma-f0-600" . At this point, in the quest for a hidden supersymmetry in the standard model, we still don't know whether it's better to look at the physical hadron spectrum or at the algebra of composite operators.

So this table at least illustrates the idea - that by pairing up quarks, you get combinations with the quantum numbers of all the standard model elementary fermions. But the exact principles on which the table was assembled are very naive, and its properties may change considerably as it become more physical. That is, we could construct an extension of Miyazawa's original hadronic supersymmetry scheme, or an electroweak extension of a dual resonance model, and then see what the tabulation of composite states/operators looks like.

 

[arivero]

I will crosscheck the hyper-bootstrap pairings during the week end, at a first glance they seem to be working well? Have you taken care of separating the I=1 and I=0 weak isospin combinations, for the L-L sector?

The reading of Huerta is interesting. It is clear that there are some differences between u-type and d-type, so we can expect uu to have different role than, say, dd. I am thinking that some detail about being in the fundamental or the adjoint representatios should emerge somewhere, after all we are expecting dd and ud to partner with particles in the fundamental representation of the gauge group, while uu should parnert with particles in the adjoint of the unbroken gauge group (and on the other hand, charged under electromagnetism, so somehow in a fundamental repr of U(1))

Also, which is the difference, Huerta-wise, between electromagnetism and hypercharge? Does the former use real representations, while the later uses real ones? Could it be relevant?

 

[arivero]

Working a little bit with the table, it seems that substituting the naive symmetrisation by a better one will save the day. For quarks, the d comes in packages of 6 and 6, and then u comes in 9 plus 6. But the later 6 is in the diagonal, so the full, unsymmetrised, box actually "12 and 12" for the d and "18 and 6" for the u, which restores the counting and your previous statement where the hyperbootstrap is four times the superbootstrap.

I guess that what we want to go down fro 24 to six is to use the traditional spin sum for 1/2 particles 2x2=3+1 and reject the triplet, isolating the scalar singlet. Some similar trick could be worked out for isospin, but here the it makes sense to use the real thing. Still, it will be amusing in the up sector.

For the charged leptons, some extra work seems to be required: we have (6+6)+6, or if we consider the full box, (12+12)+12. Perhaps the first sum must be symmetrised on its own, reducing to one half. This extra work is strange, because in the superbootstrap the charged lepton sector is similar to the d sector. It could be related to the point of having particle-antiparticle here, and then it is always possible to distinguish each particle, while in the quark sector we can have undistinguible particles.

For the quarks, for all but two outcomes, there are six ways to do it. What we really want is three (the number of generations), but perhaps we can think of pairing the six off in superposition. For (1/3,1/2) and (-1/3,-1/2), there are nine options, as if we want three elements in superposition per flavor, rather than two. Curiously, these are states with electric charge of magnitude 2/3, so maybe we should group them into superpositions with two, two, and five elements, with the five-part superposition being the top.

For the leptons, characteristically there are 12 (6+6) or 13 (4+9) ways to obtain any given outcome. The exceptions are (+/-2,0), but these can be paired up with half the (0,0)s - we have 26 of those. Anyway, here it seems we want four elements in a superposition corresponding to a single standard model species of fermion (specified at the flavor, handedness, (anti)particle level), rather than two.

 

[mitchell porter]

Some more attachments which should make it easier to compare super and hyper...

I have some new thoughts about how to make this work in field theory. The important point is that, along with the option of simply identifying leptons as mesinos and quarks as diquarkinos, one may also regard mesinos and diquarkinos as extra states which mix with fundamental quarks and/or leptons, with which they share electroweak quantum numbers. This appears to require terms in the Lagrangian that combine a chiral fundamental field with a composite of the opposite chirality. That is, together with, or instead of, ordinary mass terms like "qbar_L q_R", one also has "qbar_L D_R", where "D" is the composite which mimics the quark "q". This is a way for the diquarkinos corresponding to udscb to mix with them, contributing some or all of their mass. (In the simplest scenario, the top and all the leptons are wholly composite.)

 

[arivero]

Going to mesinos and diquarkinos has the advantage that we don't worry anymore that the supersymmetry generator violates the barion number (actually, B-L). On the other hand, the fundamental view induces to go even beyond the hyper-bootstrap to the, er, LR-bootstrap?, using B-L, I3R and I3L as the quantum numbers. In this case the electric charge formula is, if I recall correctly

Q= 1/2 (B-L) + I3R + I3L.

Where for instance a uR quark has B=1/3, I3R=+1/2, I3L=0. While a, say, eL lepton has L=1, I3R=0 and I3L=+1/2.

Some more attachments which should make it easier to compare super and hyper...

Yup, it is clear now. As expected, the down squark and charged slepton sectors are way less problematic, sneutrinos are midly problematic (they are off diagonal, so it only happens that you get some extras if you do not use the decomposition 24+1 of SU(5) irreps) and the diagonal sector, the really intriguing one, is the up squark and the extra, "H" sector.

 

[arivero]

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.

I have looked again the article of Csaki, Shirman, Terning, as well as Terning textbook --which I happened to buy randomly in January, in a generic library (!) in Paris-- chapters about duality. I am very surprised that they have not found the sBootstrap effect; even in some cases it is reasonable, in their context, to separate a particular quark from the rest, as we do. Same worry with Luty, and with other people who were taking some advanced look to composites: Alex Pomarol, Flip Tanedo,...

 

[arivero]

Some more attachments which should make it easier to compare super and hyper...

It seems that the reduction from hyper down to super works in a sequential way:

first, we reduce the four copies down to one. This should be to take the singlet LR-RL of each of the boxes.

Then, we get the symmetrical combination, say ab+ba, of the pairs. This is the "15 out of 5x5=15+10" in my language, or just the upper triangular matrix including the diagonal, in your drawing.

I still don't get why the procedure does not commute, if you first do the triangular matrix, then it becomes obscure how to do the RL-LR selection. I hate tensor products.

 

[arivero]

Interestingly, if one goes finer than hyper-, down to Mohapatra-Pati-Salam, the added charges do not bootstrap explicitly: the single quarks have "hypercharges" (actually, L and R isospins) either (1/2,0) or (0,1/2). The charges of L and R will add, so the composites can have only an integer sum, one or zero --via (-1/2,1/2)--. What is happening, then? That the susy operator, seen from the M-P-S point of view, violates barion-lepton number, but as it preserves electric charge, it must also violate I3 isospin proyection.

In the hBootstrap, all of the barion-lepton number is hidden as a piece of the hypercharge, so this violation is not always seen, because it is internally compensated inside I.

(Mitchell, should we write some note about all of this, more systematic that the forum thread?)

As a lateral note, while reading on GUT models, I have been amused by the way that SU(5) GUT makes its "composites" for the 10 representation, building from two 5s.

 

[mitchell porter]

I think a proof of concept (in field theory or string theory) would be desirable first: if not a realization of the full sbootstrap, then at least a demonstration of a mechanism that could plausibly make it work.

 

[arivero]

I think a proof of concept (in field theory or string theory) would be desirable first: if not a realization of the full sbootstrap, then at least a demonstration of a mechanism that could plausibly make it work.

I see your point. We have an algebra, but we don't have a mechanism, so it is still only math -and a naive one, for math-, not physics.

 

[mitchell porter]

Another approach doesn't involve supersymmetry at all, but instead a new ultrastrong confining force. You would start with udscb quarks, which also have "ultracolor" charges, and one or more further fundamental fermions - I'll call them n, n', n"... - which have ultracolor charge but not color charge, i.e. they feel the ultrastrong force but not the strong force. Under this interpretation, the mesinos and diquarkinos are not superpartners of mesons and diquarks, they are "ultrabaryons", baryons of the ultrastrong force, with one or more of the n fermions present along with the two quarks (i.e., if N is the rank of the ultrastrong gauge group, then there would need to be N-2 of the n particles in the ultrabaryons relevant for the sbootstrap). Leptons would still be mesinos, and quarks could mix with diquarkinos, but all the other apparatus of supersymmetric theories (gauginos, higgsinos) wouldn't be relevant.