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

mitchell porter

I was looking at notes from a recent talk by Adi Armoni, 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.

arxiv:0901.4508 might be the best place to start, especially for the references - the two papers by Sagnotti, and also Corrigan-Ramond. arxiv:hep-th/9906055 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.

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 a guess at the representation of a diquark-diquark string. 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.

Holographic QCD is a work in progress. "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 phenomenology there, and also AdS/QCD. 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

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 topcolor supposed to help? (There was a recent paper 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 open strings - 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 weak hypercharge. The basis of the numerology comes from adding the electric charges of the quarks in order to obtain the charges of the composites, but in the standard model, electric charge is weak isospin plus half the weak hypercharge, according to the Gell-Mann–Nishijima relation, and the weak hypercharges, which ought to be more fundamental than the electric charges, have a rather different pattern. 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

'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

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

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

That's an interesting idea. See Figure 1 here... 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: slide 14 here says the best opportunities for something more than pure top to show up, is in the vertex for four right-handed tops.

mitchell porter

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: how the sbootstrap could work, and mode-counting for MSSM electroweak sector.

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 the GUT perspective for a moment, it's interesting that E6 has a SU(3)^3 subalgebra.

mitchell porter

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 "M2-brane" thread.

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 Heckman and Vafa's explanation for the structure of the CKM matrix, 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 possess a residual symmetry, resulting from "dividing out" by the top in a larger symmetry. And the 168-element symmetry group of the Fano plane, PSL(2,7), is actually a subgroup of SU(3) which sometimes turns up in theories of flavor symmetry. (In the literature, it's often called "Delta(168)".)

arivero

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

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.