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

[arivero]

Note that recently Hill has started to use the expression "scalar democracy" for an idea of composite scalar sector very in the spirit of the sBootstrap, but at Planck scale. See section III A of https://arxiv.org/abs/2002.11547 for an instance.

Is not Hill doing the exact opposite? He is binding the top (and I am not sure if all the top - light quarks pairs too). While we need to bind all the non-top pairs.

 

[arivero]

Ah no, he uses all the sectors. Interesting. So the sBootstrap is the complementary subset?

 

[mitchell porter]

Well, the idea of the sBootstrap in its essence (please correct me if I misrepresent it) is that by considering superpartners of diquarks and mesons formed from the five light quarks udscb, you get all the fundamental fermions of the standard model. So first you have to add supersymmetry to Hill's scenario. But okay, maybe we can do that.

More vexing is the circularity of the sBootstrap with respect to the light quarks themselves. One way around this is to think in terms of UV and IR. The "fundamental" udscb can be UV degrees of freedom, and the "phenomenological" udscb can be IR degrees of freedom. To me this suggests Seiberg duality, and Strassler's 1995 paper in which he describes deforming N=2 Nc=3 Nf=6 super-Yang-Mills, to get an N=1 theory in the IR which has emergent meson superfields. It's as if we want a version where one of the six flavors has a mass even in the far UV, while the others remain massless, but in the IR we still get back six quark flavors as well as emergent leptons.

If we follow this logic, it means out of Hill's "spectrum of composite states", we only have those formed from quark fields, since in the UV where the binding occurs, only quark fields exist. The leptons will emerge in the IR, as superpartners of Hill's (1,2,1/2) states.

 

[mitchell porter]

I have just run across a 2019 paper from Japan that we seem to have missed, "Dynamical supersymmetry for the strange quark and ud antidiquark in the hadron mass spectrum". As with hadronic supersymmetry, this is not about fundamental supersymmetry, it's about an emergent symmetry that involves a boson and a fermion.

There are some novelties here. The authors get somewhere by treating the strange quark and the ud antidiquark as having about the same mass; this allows them to predict that certain multiplets of baryons (that form representations of the emergent supersymmetry) also have about the same mass. However, they are talking about the constituent mass of the strange quark, not the current mass.

Also, there is no intimation that the masses are similar for any deep reason. Nonetheless, it suggests an interesting refinement of an idea expressed earlier in this thread. Is there an infrared theory derived from the standard model, one that includes leptons, mesons, diquarks, and constituent quarks, that realizes the supersymmetry of the sBootstrap?

 

[mitchell porter]

Some recent explorations:

I was worrying about the baryon number of a "quark-diquark superfield". I don't know how it could be, that the fermionic and bosonic components of a supermultiplet, could differ in quantum numbers other than spin.

In looking around, I discovered that Miyazawa's 1966 paper that introduced hadron supersymmetry, is actually called "Baryon Number Changing Currents"! Some parts are evocative but unfortunately I don't understand the old paradigm of "current algebra".

One approach to baryon number is topological: the winding number of a skyrmion. Usually these are obtained from a 2-flavor chiral model. This is an opportunity to mention a few facts about chiral symmetry. Mathematically you can write down chiral symmetry for four or five flavors, but the heavy quarks break it so badly that it's basically useless. So chiral symmetry in our world really only applies for the three light flavors.

From a sbootstrap perspective there's an interesting twist. As mentioned in earlier comments, since pions, kaons and eta mesons are made of light quarks, they are goldstone bosons of chiral symmetry breaking; and in seeking superpartners for them, one may use the paradigm of quasi goldstone fermions.

Heavy mesons - containing one or more heavy quarks - are not modeled as goldstones. However, heavy quarks very naturally allow for certain forms of hadronic supersymmetry, e.g. heavy quark + light antiquark, and heavy quark + light diquark, have some similarities. Whether this could be unified with the preceding form of supersymmetry, I can't say.

Returning to chiral symmetry, nucleons are usually constructed as 2-flavor skyrmions. They can still be obtained in the 3-flavor chiral model; see the appendix of Witten's "Current algebra, baryons, and quark confinement".

There is a technical pitfall associated with these 3-flavor skyrmions. Skyrmions are often used as models of nucleons, in an approximation where the number N of QCD colors is treated as large. This is 't Hooft's planar limit, in which planar Feynman diagrams dominate. This is OK for two flavors, but when you have three flavors, considering the wrong large-N "baryons" will give you models of the proton in which the valence quarks can be strange quarks, which is wrong. So you have to look at a special subset of the large-N 3-flavor baryons, to obtain valid models of the nucleon, in 3-flavor large-N QCD.

It turns out this situation has an analogue, in another relative of QCD that has already been considered in this thread, "orientifold field theory". This is SU(N) Yang-Mills with a fermion in the "antisymmetric two-index" representation. It provides a model of hadronic supersymmetry, in which the meson is an oriented bosonic string, and the baryon is an unoriented fermionic string, i.e. string with a fermionic charge smeared along it. This field theory can be obtained by "orientifolding" a string theory. For many details, see this big review of the subject by Armoni, Shifman, and Veneziano.

The promised analogy is that the skyrmion in orientifold field theory is something different and more complicated than the simple unoriented fermionic string. This may all seem rather esoteric, but it may end up mattering, e.g. for the right treatment of baryon number in hadronic supersymmetry.

Orientifold field theory, in its simplest form, is related only to one-flavor QCD. However, the big review by Armoni, Shifman, and Veneziano, has something to say about obtaining three-flavor QCD too (from "orienti/2f theory"). Meanwhile, one-flavor baryons have been the subject of recent theoretical progress - see recent comments in this thread about work by Komargodski and by Karasik.

Basically, Skyrme found that multi-flavor baryons could be found as topological solitons in a sigma model of pseudoscalar mesons. Komargodski recently obtained single-flavor baryons as edge excitations of eta-meson membranes. And Karasik unified the two, by showing (?) that single-flavor baryons can be obtained from the sigma models employed by Skyrme and his school, by adding the right vector mesons. It's probably related to the fact that single-flavor diquarks are vector diquarks.

Just to round out this discussion, I'll mention that Fiorenza, Sati and Schreiber had a paper late last year, part of their quest for the proper formulation of M-theory, in which they claim to get a kind of supersymmetric 2-flavor skyrmion, on an M5-brane near an orientifold plane. And they cite hadron supersymmetry and holographic vector mesons as an inspiration.

 

[arivero]

Some recent explorations:
...

In looking around, I discovered that Miyazawa's 1966 paper that introduced hadron supersymmetry, is actually called "Baryon Number Changing Currents"! Some parts are evocative but unfortunately I don't understand the old paradigm of "current algebra".

...
Just to round out this discussion, I'll mention that Fiorenza, Sati and Schreiber had a paper late last year, part of their quest for the proper formulation of M-theory, in which they claim to get a kind of supersymmetric 2-flavor skyrmion, on an M5-brane near an orientifold plane. And they cite hadron supersymmetry and holographic vector mesons as an inspiration.

Funny.

From a sbootstrap perspective there's an interesting twist. As mentioned in earlier comments, since pions, kaons and eta mesons are made of light quarks, they are goldstone bosons of chiral symmetry breaking; and in seeking superpartners for them, one may use the paradigm of quasi goldstone fermions.

Heavy mesons - containing one or more heavy quarks - are not modeled as goldstones.

Ah, but what is a heavy quark anyway?

However, heavy quarks very naturally allow for certain forms of hadronic supersymmetry, e.g. heavy quark + light antiquark, and heavy quark + light diquark, have some similarities. Whether this could be unified with the preceding form of supersymmetry, I can't say.

 

[mitchell porter]

Koide's latest is a five-flavor preon theory! Although he only gets one generation at a time, and needs three further "family preons" to get three generations. And while some composite states are two flavor-preons plus a family preon, others are one flavor-preon plus two family-preons - whereas, in the sbootstrap, everything has two flavor-preons... On the positive side, he's working with the Weyl fermions of the full standard model, rather than just the Dirac fermions of SU(3) x U(1) physics.

This should be compared to his original preon theories, the sbootstrap, our attempts at hyperbootstrap, the "string roadmap" from #239 forward, etc. (Just in case, I'll also mention a recent paper on "SU(5)_L x U(1)_Y electroweak unification".)

 

[ohwilleke]

Koide's preon paper is interesting, although using eight preons to explain the 12 fermion and 3 boson fundamental masses in the SM doesn't seem like that big of an improvement (and you can already get one of those boson masses from SM electroweak theory with ratios of EM and weak force coupling constants, so there are really only 14 free masses, and the original Koide's rule gets it down to 13 free masses).

Yershov's preon papers were IMHO some of the most notable ones that I've seen (although my Wikipedia article on Yershov was stricken for lack of notability (although the late Marni Dee Sheppeard's work also caught my eye). The first paper takes on the SM fermions, the second takes on the SM bosons. Yershov's papers on the subject were:

The First Paper

Fermions as topological objects
Authors: V. N. Yershov
Comments: Latex2e, 20 pages, 12 figures, 3 tables, (V8: formulae compactified)
Subj-class: General Physics

A preon-based composite model of fermions is discussed. The preon is regarded as a topological object with three degrees of freedom in a dual (3+1)-dimensional manifold. It is shown that dualism of this manifold gives rise to a set of preon structures, which resemble three families of fermions. The number of preons in each structure is readily associated with its mass. Although just a sketch, our model predicts masses of fermions to an accuracy of about $10^{-6}$ without using experimental input parameters.

The Second Paper

Date: Thu, 16 Jan 2003 09:54:57 GMT (18kb)
Date (revised v2): Fri, 7 Mar 2003 18:07:30 GMT (18kb)

Neutrino masses and the structure of the weak gauge boson
Authors: V.N.Yershov
Comments: LaTex2e, 4 pages (V2: minor linguistical corrections)
Subj-class: General Physics

It is supposed that the electron neutrino mass is related to the structures and masses of the $W^\\pm$ and $Z^0$ bosons. Using a composite model of fermions (described elsewhere), it is shown that the massless neutrino is not consistent with the high values of the experimental masses of $W^\\pm$ and $Z^0$. Consistency can be achieved on the assumption that the electron-neutrino has a mass of about 4.5 meV. Masses of the muon- and tau-neutrinos are also estimated.

Yershov's is the only preon model that really nails the particle masses (and does so in a quite innovative way). A figure from Yershov's first paper above:

It doesn't really do a great job of explaining why there are only three generations, but there are ways to get there (e.g. too many preons can't hold together, or the W and Z boson widths that facilitate the changes between states don't allow for any preon composites with a width less than the top quark).

There is some wiggle room in the theory to improve the fit, as the first paper notes, as well:

The results presented in Table 2 show that our model agree with experiment to an accuracy better then 0.5%. The discrepancies should be attributed to the simplifications we have assumed here (e. g., neglecting the binding and oscillatory energies, as well as the neutrino residual masses, which contribute to the masses of many structures in our model).

Alas, the fits have not aged very well.

A sort of composite Higgs mass relationship:

Yershov's paper didn't take on the Higgs boson, which wasn't confirmed to exist at the time that his papers were posted. But it isn't too difficult to extend it to include a massive Higgs boson as a composite particle in a manner very different from technicolor theories.

The hypothesis that two times the rest mass of the Higgs boson mass is equal to the sum of the electroweak boson rest masses (W+, W-, Z and the photon) is consistent with the experimental data at better than 2 sigma and would imply a best fit binding energy of 723 MeV. If the W boson has about 2 sigma less rest mass, as global electroweak fits to the W boson mass prefer, the match is even tighter and less binding energy is required.

Since bosons obey Bose statistics, the binding energy wouldn't have to be nearly so high as in a composite particle made up of fermions since they can be in the same place at the same time. So, the binding energy would just need to be slightly more than what is necessary to hold the EM force between the W+ and W- together.

This binding energy is ballpark on the same order of magnitude of the EM contribution to the proton mass. A June 18, 2014 paper estimates that differences in electromagnetic field strength between the proton and neutron account for 1.04 +/- 0.11 MeV, but the W bosons are much more massive than the up and down quarks by a factor of about 16,271. After adjusting for 723 MeV of binding energy v. 1.04 MeV of binding energy, and using a greater distance between the W+ and W- to reduce the amount of binding energy to overcome the EM force, this is equivalent to a distance apart 4.83 times as great in a two Higgs boson pair as the average distance between quarks in a proton. This is not an implausible order of magnitude match.

 

[ohwilleke]

I'll also mention a recent paper on "SU(5)_L x U(1)_Y electroweak unification".

The paper notes in the introduction:

The main result - that allows for a plethora of new degrees of freedom beyond those coming from the Standard Model (SM) - regards the mass spectrum of the model.

This is a serious bug and not a feature to brag about.

 

[arivero]

Motl has mentioned/reviewed a recent interview with John Schwarz for the oral histories collection
https://www.aip.org/history-programs/niels-bohr-library/oral-histories/45439
and his reminiscence of earlier theories is short:

So we called the theory the dual pion model. But anyway, that’s just a historical thing which is very forgettable, because the modern interpretation is entirely different.

The general topic is mentioned as dual resonance theory. So I have taken some time to review inspire-hep looking for the alternative names that are the topic of this thread, just as a refresher

1969 K. Bardakci(UC, Berkeley), M.B. Halpern(UC, Berkeley) Possible born term for the hadron bootstrap
1969 M.B. Halpern(UC, Berkeley), J.A. Shapiro(UC, Berkeley), S.A. Klein(Claremont Coll.) Spin and internal symmetry in dual feynman theory
1970 K. Bardakci(UC, Berkeley), M.B. Halpern(UC, Berkeley) New dual quark models (this is the string bit theory, is it? or is it more?) (topcited > 300)
1971 J.H. Schwarz(Princeton U.) Dual quark-gluon model of hadrons "Our proposal is to interpret the Ramond fermions as quarks and the "Dual-pion model" bosons as gluons"
1971 M.B. Halpern(UC, Berkeley), Charles B. Thorn(UC, Berkeley) Two faces of a dual pion - quark model. 2. Fermions and other things
1971 A. Neveu(Princeton U.), J.H. Schwarz(Princeton U.) Quark Model of Dual Pions (topcite > 500) Interacting pseudoscalar pions are incorporated into Ramond's model of free dual fermions. By considering the emission of N−1 pions and factorizing in the quark-antiquark channel, we recover the same N-pion amplitudes as were proposed in a previous paper.
1971 Stephen Dean Ellis(Caltech) A Dual Quark Model with Spin
1971 I. Bars(Yale U.) Degeneracy breaking in a ghost-free dual model with spin and su(3)
1972 P.G.O. Freund(Imperial Coll., London and Chicago U., EFI) Quark spin in a dual-resonance model The foundations are laid for a dual-resonance model with a spectrum characteristic ofU6×U6×O3 symmetry. The model provides an automatic mechanism for the breaking of the collinearU6×O2 symmetry. The states on the leading Regge trajectory with the exception of the lowest (« ground ») state are all parity doubled. It is argued that there may exist « mesonic » strings with a quark at one end and anSU3-singlet spin-zero boson at the other end. These complex hadrons would have all the quantum numbers (half-integer spin, nonvanishing triality, etc.) of quarks, while not being really quarks (e.g., a baryon would not be built of three of them).
1972 Edward Corrigan(Cambridge U., DAMTP and CERN), David I. Olive(Cambridge U., DAMTP and CERN) Fermion meson vertices in dual theories
1972 S.D. Ellis(Fermilab) Regge pole model of pion nucleon scattering with explicit quarks
1973 K. Bardakci(UC, Berkeley), M.B. Halpern(UC, Berkeley) DUAL M - MODELS
1973 John H. Schwarz(Caltech) Dual resonance theory ...A modification of the Veneziano model incorporating SU( N ) symmetry in a dynamical fashion is shown to have critical dimension 26− N[/size]
1973 L. Brink(Durham U. and Goteborg, ITP), D.B. Fairlie(Durham U.) Pomeron singularities in the Fermion meson dual model
1974 J.H. Schwarz(Caltech) Dual quark-gluon theory with dynamical color A modification of a previously proposed dual resonance theory of quarks and gluons is presented. It consists of incorporating new oscillator modes carrying color indices. The specific properties of these operators and the way they are included into the theory are completely determined by various consistency requirements. This modification of the theory has two important consequences. First, quark statistics are properly taken into account. Second, the critical dimension of space-time is reduced to d = 10−2 N , where N is the number of colors. Thus, the physically preferred choices N = 3 and d = 4 are compatible.
1974 L. Brink(Goteborg, ITP), Holger Bech Nielsen(Bohr Inst.) Two Mass Relations for Mesons from String - Quark Duality
1975 Joel Scherk(Caltech), John H. Schwarz(Caltech) Dual Field Theory of Quarks and Gluons " The 10-dimensional space-time of the spinor dual model is interpreted as the product of ordinary 4-dimensional space-time and a 6-dimensional compact domain, whose size is so small that it is as yet unobserved. This leads to an SU(4) symmetry group with quarks in both a 4 and a 4 multiplet. " (topcited > 200 )
1976 M. Ademollo(Florence U. and INFN, Florence), L. Brink(Goteborg, ITP), et al, Dual String Models with Nonabelian Color and Flavor Symmetries

It seems that dual quark in the early seventies referred to the idea of adding flavour-spin SU(12) or u(6) or similar beasts in order to produce all the mesons. So it stands to reason that Schwarz considers this denomination a different way from pure string theory. He does not see any relationship with SO(32) strings or the like. So his 1971 paper prefers to use the title "quark model of dual pions" to stress the diference with group theoretical flavour games.

1972 is the year of the basic QCD paper https://arxiv.org/abs/hep-ph/0208010
Current Algebra: Quarks and What Else? Harald Fritzsch, Murray Gell-Mann
and then SU(3) colour was still denominated quark-gluon theory, it seems.

In 1975 paper, the approach does not include pions anymore, it is "gluons", and the conclusions explain that "The approach of this paper departs from the conventional philosophy of trying to use dual models to construct a ·more or less realistic approximstion to the hadron S matrix. Instead, we are suggesting the use of the spinor dual model as an alternative kind of quark-gluon field theory in which the input fields have color and presumably do not correspond to physical particles."

 

[arivero]

About the mesons, while reading this old note of Neumaier https://www.physicsoverflow.org/27965/ I see that some consideration should be given to the difference between charged and neutral mesons, because some of the neutral mesons can decay even in the absence of weak force.

 

[mitchell porter]

One recurring theme in this thread, is the idea that the standard model might arise as the low energy limit of a theory which, at high energy, is a super-QCD (with quark superfields). I have run across a paper (and accompanying video) which studies a regime of SQCD which is promising from this perspective.

The author's objective is actually to prove properties of QCD with various numbers of flavors, as a limit of the corresponding N=1 theory. The question is, what to do with the squarks and gauginos, which are not part of QCD. The answer is to use a special method of susy breaking, anomaly-mediated supersymmetry breaking, which makes the squarks and gauginos massive. An interesting technical detail is the analogy between AMSB, and QCD in curved space. The lagrangian for QCD in curved space is simply the usual lagrangian, multiplied by a universal factor of sqrt(-g), where g is the metric. AMSB has a similar coupling, but it's to a fermionic deformation of a superspace, i.e. a generalized geometry with a fermionic direction. See around 37:00 in the video.

From a sbootstrap perspective, a key moment is on page 3 of the paper. The superpotential has two minima and the author can't work out which is lower apriori. However, one has massive mesinos and the other one has massless mesinos. The author wants to obtain non-supersymmetric QCD and so he opts for the one with massive mesinos (since they can drop out of the effective theory, once they become massive enough). However, from our perspective, we want light mesinos, since that's where the leptons are to come from.

It's QCD with 3 colors and 3 flavors that is being discussed, so these calculations should be compared with the work from the 1980s, mentioned starting at #222 in this thread. (By the way, back at post #49, I actually mentioned AMSB as a promising approach.)

 

[mitchell porter]

Diquarks (and any "diquarkinos") are in the adjoint representation of QCD. QCD with fermions in the adjoint representation is sometimes studied via supersymmetric QCD, since gluons are also in the adjoint, and therefore so are their gluino and sgluon partners. Part 1 of a paper from 2018 reviews some of these relationships. The paper's focus is on SU(2), but Emily Nardoni at Strings 2022 promises a forthcoming paper dealing with all SU(N).

 

[arivero]

Just for the search engines: "biquarks" and "bifermions".
https://arxiv.org/abs/2301.02425 An SU(15) Approach to Bifermion Classification.

This is Frampton's team. They suggest that diquark should be reserved for the SU(3) composite, and use biquark for elementary particles. They had already used the term "bileptons". It is a brief not, sparse, suggesting that SU(15) is an interesting group to work with.

This thread post #254 and post #244 suggest to go down to the 224 and 105 SU(15), but then go special getting the squarks from the (15,3) down the 105, and the sleptons from the (24,1) of the 224 and we are in completely different decompositions. Or more properly, Frampton's team go the discovery way, while our posts were just evaluating Slansky formulae. I can not see the advantage of doing differently, the other way also produces +4/3 particles. They go their way because it is still the idea of having a standard model family all inside a 15 representation, that Frampton defended in the past century.

Another call to the SU(15) door comes from Dobrescu arXiv:2112.15132 arXiv:2211.02211 but it overloads to SU(15) x SO(10) to combine preon and standard model charges so again I fail to relate their decompositions with ours. It would be more interesting if they were able to uplift -or rearrange- it towards say SO(16)x SO(16) or other stringy connections.

 

[Adrian59]

Another call to the SU(15) door comes from Dobrescu arXiv:2112.15132 arXiv:2211.02211 but it overloads to SU(15) x SO(10) to combine preon and standard model charges so again I fail to relate their decompositions with ours. It would be more interesting if they were able to uplift -or rearrange- it towards say SO(16)x SO(16) or other stringy connections.

As you will no doubt surmise from my question, I am not a string theorist, though I have read most of Green, Schwarz and Witten's book. My question is that from an understanding of the standard model of particle physics, the number of generators of a Lie group is equal to the number of force exchange bosons, so by going to ever larger groups like S0(32) for heterotic string theory or SU(15) one gets either 496 or 224 generators, respectively. Do these nearly all represent undiscovered bosons? If so, it makes the non-discovery of supersymmetric particles look trivial.

 

[arivero]

Adrian, if you have read the GSW you will be already suspecting that they do not get the SM gauge groups straight from the big ones, but they go to special shapes in compactification, all that brane stuff. The book of Ibañez is better source for this way that the GSW tomes. Perhaps you have here a good intuition that going to D-brane intersection and special configurations is the way to avoid the need of discovering too many generators, and associated fermions. They can make the case that only the zero modes, the massless particles in the high dimensional representation, have some sense in the low energy, and then they can even purge them via the configuration.

 

[Adrian59]

Perhaps you have here a good intuition that going to D-brane intersection and special configurations is the way to avoid the need of discovering too many generators, and associated fermions. They can make the case that only the zero modes, the massless particles in the high dimensional representation, have some sense in the low energy, and then they can even purge them via the configuration.

I suppose I should have mentioned that I only read volume 1. I don't recall any brane stuff in that, maybe that is in volume 2. Of course they (GSW) do talk about compactification in volume 1. You said that they only make sense of the massless particles, and I presume you mean bosons, but the SU(2) and SU(3) bosons have mass. Even so, I am very suspicious of complex mathematical theories that somehow just manage to rid themselves of all the spurious baggage just at the end. I am sure nature is not so profligate.

 

[arivero]

No, you are right they are not about Branes in GSW. It was a later development, starting with some ideas from Polchinski if I recall correctly.

They were also looking for massless fermions. I think the intuition was initially Kaluza-Klein, where a massive particle in 4D is just a massless particle in 5D. The final idea being that any particle to appear in low energy should be massless in the 10D (or 11D if sugra/mtheory) formalism.

 

[mitchell porter]

From a recent lecture by Witten on confinement (around 29:50), I learned how diquark (quark-quark) interactions fit into one of the most potent theoretical frameworks connecting QCD to string theory, the "1/N expansion". This is a model due to 't Hooft, which treats gluons as little ribbons, and quarks as currents on the edges of the ribbons.

The focus in 1/N theory is mostly on "planar" Feynman diagrams built up from these ribbons - they are called planar if you can draw them without the lines crossing. These planar meshes of gluon ribbons build up into sheets that behave like strings! And more complicated graphs in which the ribbons also form bridges across the diagram, correspond to multiloop string diagrams. You can recover something resembling the topological expansion of perturbative string theory, by resumming these graphs according to their topology.

N refers to the number of colors. There is a factor of 1/N for each topological loop in the resummed theory. The expansion works best for large N, but even for the real-world case of N=3, the 1/N expansion has some validity... But the real apotheosis of the 1/N expansion came with AdS/CFT. Here, N is the number of colors in the boundary gauge theory, and the correspondence to a string theory in the bulk is believed to be exact.

Anyway, the interactions in planar 1/N theory are between quark and antiquark, because that assigns color-anticolor to gluons as required. What Witten points out (but this probably goes back to 't Hooft's original work), is that even with a quark-quark interaction, you can still get color-anticolor current for your gluon, if the ribbon is twisted. But this will add a 1/N factor to the amplitude, because the twist in the ribbon breaks planarity; topologically, the ribbon adds a twisted handle to the diagram (when the diagram is considered as a discretized surface).

From Witten's perspective, this is just a step in his own contribution to 1/N theory. 't Hooft's original work described mesons, which are quark-antiquark and therefore "planar". Witten extended the framework to N-quark baryons by noting the 1/N force between any pair of quarks in the baryon, and that any individual quark is therefore bound to the collection of N quarks by an overall force of order 1 (1/N times N). Then he obtained the baryon as a soliton in the meson field theory, this tied back to Skyrme's work on skyrmions, and it all became another part of QCD lore (which again is refined further in AdS/CFT).

Our interest, however, is in how this could fit into the sBootstrap, which means adding supersymmetry (and also flavor, and ultimately charge too). In this regard, one recurring problem is that, unlike a meson, a diquark is not a gauge-invariant object. For the sake of model-building, one can put off this problem by using a toy model in which the quarks are scalar bosons rather than fermions, or in which there are only two colors - in both these cases, the diquarks are gauge-invariant. But eventually one needs a framework that deals with the real case of interest. We've surely covered a few candidates in the course of this thread...

 

[ohwilleke]

From a recent lecture by Witten on confinement (around 29:50), I learned how diquark (quark-quark) interactions fit into one of the most potent theoretical frameworks connecting QCD to string theory, the "1/N expansion". This is a model due to 't Hooft, which treats gluons as little ribbons, and quarks as currents on the edges of the ribbons.

The focus in 1/N theory is mostly on "planar" Feynman diagrams built up from these ribbons - they are called planar if you can draw them without the lines crossing. These planar meshes of gluon ribbons build up into sheets that behave like strings! And more complicated graphs in which the ribbons also form bridges across the diagram, correspond to multiloop string diagrams. You can recover something resembling the topological expansion of perturbative string theory, by resumming these graphs according to their topology.

The notion of string theory (and maybe even supersymmetry), as an emergent theory in which composite structures of SM fundamental particles are the strings (or super partners) is very elegant and attractive. It's exciting even.

This ansatz retains the mathematical insights and benefits of these theories (and explains why they can produce results that have any validity or usefulness, and it also explains and quantifies why they don't work perfectly, since the N is finite and small, not infinite), without the conundrums of trying to narrow down the landscape of vacua to find one that replicates the SM or having to escape swampland. When the SM is fundamental and prior, the possible string theory parameters are fixed by the SM instead of the other way around.

This deprives string theory of the center stage role as a TOE that it has aspired to, of course. But, any help in amplitudology calculations has considerable value and salvages what would have otherwise been a lot of wasted effort by string theorists. Finding some use for this theory is good, because it has become increasingly clear that string theory is not the TOE answer that theorists were looking for, for a variety of reasons. If all string theory could provide was a failed TOE effort, it would all have been a total loss in terms of the immense efforts of some of our planets brightest minds devoted to it for decades.

This paradigm shift also clears the decks to go down another path to explain why the SM has the particle content and experimentally measured parameters that it does unburdened by the baggage of string theory and supersymmetry.

Could the string theory graviton itself actually be an emergent or composite entity? Maybe Verlinde and Mach were on the right track. What if gravity is not just computationally, but literally QCD squared force, due to a graviton being a composite of a pair of vector bosons?

On the other hand, if string theory is not fundamental, we are still adrift in terms of resolving the infinities and problems associated with the SM's tendency to think of fundamental fermions and bosons as point particles and finding a quantum gravity theory that works, which were part of what motivated string theory in the first place.

But contrary to its advocate's claims, surely string theory is not the only mathematically viable way to address these issues, even if we haven't thought of good alternatives or the "right answer" yet.

 

[arivero]

Verlinde and Mach were on the right track. What if gravity is not just computationally, but literally QCD squared force, due to a graviton being a composite of a pair of vector bosons?

https://inspirehep.net/literature/1395565 did u mean this link?

 

[arivero]

Thinking about, we keep speaking about string theory, but a good starting point could be the MSSM with unbroken SUSY, and then just break the higgs pretty maximally, with infinite mass for W and Z0 so that the fermions have only SU(3)xU(1) interactions.

Is there any paper or textbook doing this? Any reference is appreciated.

I think that leaving out the weak decays we can also ignore the need of the Higgs as a whole, but I could be missing something about anomalies here.

Anyway, the logical continuation is to set the three multiplets as described elsewhere in this thread and try to break SUSY only in a mild form:

where "standard model" means only the colour+EM part, in this case, leaving aside the weak decays for another round. And the names of the scalars are just a reference, they are just the needed superpartners of each of the three supermultiplets.

 

[mitchell porter]

I'm hoping to give a longer comment on methods of supersymmetry breaking and other aspects of the problem, but first I want to report something that I ran across just now. I'm not sure what to make of it.

Wiki describes Pierre Fayet as the first person to actually propose phenomenological superpartners. Anyway, it turns out that since the mid-1980s, he has been proposing a different version of SU(5) GUT that has some very atypical properties.

It seems to start with N=2 supersymmetric SU(5)xU(1) in 6 dimensions; then some kind of electroweak breaking occurs, that leaves what he calls an "electrostrong" symmetry. However, the electrostrong symmetry group is not SU(3)xU(1), it's an SU(4) subgroup of SU(5) (I haven't checked if it's the SU(4) from Pati-Salam).

What really caught my eye is this. Since he is starting with SU(5), along with standard model bosons, he has the X and Y bosons of grand unification. And because he has supermultiplets, he also has "Dirac Xinos" and "Dirac Yinos" with charge ±4/3 and charge ±1/3 respectively.

@arivero, did you ever run across this before? These "Dirac Xinos" have the spin and charge of the most problematic particles implied by sBootstrap combinatorics - fermions (diquarkinos) with charge 4/3, that are the superpartners of the uu, uc, cc diquarks. So it's very nice that they emerge so naturally here!

On the other hand, these are GUT gauginos, and gauginos are the particles implied by ordinary supersymmetry that are most problematic for the sBootstrap (in my opinion). There are some hints that gluinos could be useful (e.g. see #289, 292, 313 in this thread), but it's very unclear and usually I just think of them as being out of the picture for some reason (e.g. superheavy).

Fayet says some other things about his X and Y supermultiplets: the X is massless in 6 dimensions (I think because it's one of the SU(4) gauge bosons), while the Y has the mass of the W! Also, he thinks that the spin-0 Higgs is the N=2 superpartner of the spin-1 Z boson.

So to sum up, Fayet proposes an N=2 GUT in 6 dimensions, in which electroweak symmetry is broken independently of supersymmetry, so apparently the theory has a phase that is something like an unbroken N=2 d=6 "electro-strong" theory, with Dirac fermions that could be the missing piece of the sBootstrap.

I'm worried that this comes at the price of too many extra particles. (I also don't see how he gets chiral behavior in 4 dimensions.) But it's definitely on the list of models or frameworks we should study a bit, just in case it has a minimal form where everything works neatly.

Two 1980s papers to start with might be in Phys Lett B 1984 and Nucl Phys B 1984. A more recent discussion can be found in his 2015 review of the supersymmetric standard model (e.g. see page 24 for the 6-dimensional mass of his X and Y supermultiplets).

 

[arivero]

Yep I was aware, it was one of the motivations to keep hope, but I don't like that it implies a lot of extra content.

 

[arivero]

Speaking of awareness, I took a time to try to understand why diquark research is not finding the same diquarks that here. It seems my preprints use the "worse spin zero diquarks" in the nomenclature of Jaffe's Exotica. And using 5 flavours it is really the $(15, \bar 3)$.

That means, as it is pointed out in Salem's bachelor thesis (and Wilczek's preprints on the topic), that they are energetically disfavoured respect to the good and bad diquarks, which are the ones used by Miyazawa, Catto etc. I was never very worried because initially I only noticed the coincidence of degrees of freedom for leptons, and my preprints (https://arxiv.org/abs/hep-ph/0512065 https://arxiv.org/pdf/0910.4793.pdf) focused first in combinatorics and later in links to string theory. Still, it is true that the first one referenced Lichtenberg and Catto as sources of authority on diquarks.

Other point of difference with these authors is that they do not put a lot of emphasis on getting quarks and diquarks in the same supermultiplet. For Gursey and Catto, it is just a tour of force showing the usage of Jordan Algebras and octonions. For Miyazawa, the fundamental representation is just a guide to build the product. And anyway there is no coincidence in the number of degrees of freedom.

It could be of some value to consider both the combinations to obtain scalars and pseudoscalars, and see the variations in the uniqueness; perhaps there is not solution at all with the whole condition of producing same number of states with charges +2/3, -1/3 and -1. For leptons it could be, but for quarks I can not see how to produce the same number of scalars than pseudoscalars. Still, it could exist a solution with scalar diquarks, I should check.

The way to Miyazawa is better seen in the independent argument of Gao Chong-shou and Ho Tso-hsiu:

where it is clear that the idea is to use just the sum of good and bad diquarks. There is an interesting reminiscence by Sugawara that in turn quotes verbatim another from Miyazawa. In 1981, 1983, and later in 1986, Miyazawa revisited the symmetry and proposed that the quarks and leptons could be the Nambu-Goldstone particles coming from its breaking.

Looking into group theory later, six years ago -it seems- I did the SU(6) trick but not with spin up and down but with particle vs antiparticle, so this could be SU(10|55) in supergroup notation

It was fun because if one puts also colour in then it goes up to SU(30|465) and very in the realm of superstring groups, almost filling the 496.

There is an independent approach to diquarks by Golowich and Haqq that does not go very deep, but acknowledges some discussion with Witten and proposes that elementary scalars could be also interacting in the QCD soup.

My guess is that this case is already ruled out by limits on susy searches.

Also to be noted is that Georgi and Wise, in their presentation of "superflavor symmetry", consider not diquarks but fundamental scalars coming from supersymmetry or from technicolour.

 

[kodama]

Could the string theory graviton itself actually be an emergent or composite entity? Maybe Verlinde and Mach were on the right track. What if gravity is not just computationally, but literally QCD squared force, due to a graviton being a composite of a pair of vector bosons?

any specific details ? which pair of vector bosons? a qcd glue ball ?

a new force or qcd or qed?

 

[mitchell porter]

Miyazawa revisited the symmetry and proposed that the quarks and leptons could be the Nambu-Goldstone particles coming from its breaking

Mizoguchi and Yata (section II) list some of these exceptional coset models. But in these models, all the SM fermions are superpartners of "pions".

Diquarks are goldstones in 2-color QCD (you could compare equation 8b in Shifman and Vainshtein, to Table III from Jaffe, reproduced above). So in 2-color SQCD, presumably there really are "diquarkinos" among the quasi Goldstone fermions.

Shifman and Vainshtein also argue that the phenomena of 2-color QCD should have an echo in 3-color QCD. So maybe there are "diquarkinos" in 3-color SQCD too - perhaps qg͂q objects, where g͂ is the gluino - and maybe they can mix with the quarks... Something to check.

 

[mitchell porter]

1) Harun Omer, last seen in #288, returns with "Light-Front Holographic QCD from a Coherent State in String Theory". From what I understand, this is a zero-length open string attached to a brane, which is holographically dual to AdS2, and which realizes the dAFF superconformal algebra used by the Brodsky school of hadronic supersymmetry. Omer explicitly says he is returning to the original vision of string theory, e.g. that the excitations of the string should correspond to the Regge trajectories of the observed hadrons, rather than to unobservable Planck-heavy states that only matter for quantum-gravitational unitarity. He says the coherent state mentioned in the paper's title, is what allows him to obtain excited string states at the QCD scale.

It's possible that there's a mistake somewhere here. The section on phenomenology is rather terse. The abstract makes a claim ("connection exists to gravitationally dressed excited states in AdS3") which is not followed up at all. I can say that AdS2 D-brane bound states have been studied before (and see here for the M2-brane), as well as work on coherent states in string theory, so all that might help us evaluate Omer's work.

2) In #298, Urs Schreiber asked if the WZW term from chiral perturbation theory had ever appeared in a model of hadronic supersymmetry. At the time I said no. The answer is still no; but there are two papers from the mid-1970s (Hwa and Lam, non-relativistic, relativistic) in which hadronic supersymmetry is built on the Wess-Zumino algebra.

Personally I wonder if the fashionable "non-invertible symmetries" might describe some aspect of the sBootstrap flavor calculus; and there are fusion rules for WZW models (fusion rules being the original example of a non-group-theoretic "symmetry")...

 

[pavsic]

There is a significant challenge in higher-dimensional theories, including string theory, regarding how to render the extra dimensions unobservable. A commonly employed approach involves assuming that the extra dimensions are compact and small. However, we can sidestep the necessity for compactification by postulating that spacetime is a subspace of a multidimensional configuration space—specifically, the space of possible matter configurations in 4D spacetime. Instead of formulating physics in spacetime, we can formulate physics within the configuration space.

A potential avenue in this direction was explored in my talk titled "Extending Physics to Clifford Space: Towards the Unification of Particles and Forces, Including Gravity." I delivered this talk as part of the lecture series "Octonions, Standard Model, and Unification," held from February 24 to December 15, 2023. You can find more details about the series here: https://hyperspace.uni-frankfurt.de/2023/02/10/octonions-standard-model-and-unification-online/

The video recordings of these lectures can be accessed at . Specifically, the video recording of my lecture is available at .

In the talk there is a section on how string theory can be consistently formulated in a target space with neutral signature (p,q) with p=q. In that setup, the higher dimensional target space is the 16D space, with signature (8,8), of the oriented
areas/volumes associated with fundamental objects. In such scenario, one can construct a string theory without increasing the dimensionality of spacetime. One has a higher-dimensional theory without increasing the dimensionality of spacetime.

 

[mitchell porter]

Christopher Hill has a new paper on the NJL model, "Nambu and Compositeness", in which he says that Nambu "thought there was a hidden supersymmetry in the NJL model". Hill wrote his own paper on the subject ("Super-Dilatation Symmetry of the Top-Higgs System"), but to see Nambu's own thoughts on this topic, you have to go to

Dynamical symmetry breaking. Proceedings, Workshop, Nagoya, Japan, December 21-23, 1989

and click on the pdf. The first chapter is

"Model building based on bootstrap symmetry breaking"

Page 8 has the section on "quasi-supersymmetry".

Don't forget the 1993 NJL model due to Kahana and Kahana which predicted the top and Higgs masses...

 

[mitchell porter]

"Two-index SU(N) theories" by Francesco Sannino has some diquark-looking diagrams from a 't Hooft large-N expansion (pages 13-15). These theories also have a relationship to super-Yang-Mills, since the antisymmetric two-index quarks can model gluinos as well as diquarks.

The paper also mentions a kind of large-N expansion I hadn't heard before. Along with the usual large-N expansion and the two-index large-N expansion, there is now a chiral large-N expansion which seems to treat some Weyl fermions as quarks, and others as diquarks.

 

[arivero]

Finally took some time to upload to arxiv the collection of group theoretical comments about SO(32) SU(15) etc ... Not included the present discussion in thread 1063905

An interpretation of scalars in SO(32) https://arxiv.org/abs/2407.05397​

We propose an interpretation for the adjoint representation of the SO(32) group to classify the scalars of a generic Supersymmetric Standard Model having just three generations of particles, via a flavour group SU(5). We show that this same interpretation arises from a simple postulate of self-consistence of composites for these scalars. The model looks only for colour and electric charge, and it pays the cost of an additional chiral +4/3 quark per generation.

 

[arivero]

Hmm and now I notice that the argument in https://www.physicsforums.com/threads/asking-for-a-six-preon-theory.1063905/post-7102865 is a sort of counterexample to my "uniqueness theorem". It shows that if we give more freedom about the particle set, allowing for leptons, then the classic Georgi-Glashow model is able to generate all their superpartners, with one generation.

And now I wonder if all the unification groups have this property, of having a subset n such that their composites contain exactly the superpartners

 

[arivero]

I asked AdR for permision to use his old drawing; he had a colour scan somewhere in his archive

 

[arivero]

A referee did an interesting objection to the sBootstrap idea: there is no explanation of why the spectator quark is the top quark. It could similarly be the up or the charm. Honestly I do not see how to find out which one is, because we newer got a model of masses.

We speculated time ago to get the masses out of 84-dimensional representations, so with groups similar to SO(9), SU(9) or SU(12); or lacking that, some 21 or 42 dim representation. We could also try to change our 15s of SU(5) for some 10, but very peculiar. Instead of 6 (-1/3), 6 (+2/3) and 3 (+4/3),
it should have 6 (-1/3), 3 (+2/3) and 1 (+2/3).

Another approach could be to consider the sBootstrap a theory of preons and see if the ideas of Terazawa and Koide can be useful.

A third way, not considered, could be to find goldstone bosons, under the principle that they are massless. In this case I am not sure how group theory helps; I guess one must substract dimensions of the adjoint for the original and the broken group.

 

[arivero]

Thinking if it is possible to alter the masses of the scalars somehow breaking the flavour symmetries or mixing the 15 irrep with the 10, in the same way that the octect mixes with the singlet. I do not see how. But you could enjoy the drawing of this SU(3)xSU(2)

Note, if you are new to the thread, that the number of particles is equal to the number of scalars of the supersymmetric standard model, with three generations, except that we get those awful +4/3 things

It is funny to consider the transformation from particle to antiparticle at the preon level. Look at the Q=+1/3, it is a triangle (ud,us,ub) and another (cd,cs,cb). If you change c to c, the point is mapped to the Q=-1 triangle, if you change d to d, it is mapped to the Q=+1.

And now look Q=-2/3. The internal points are mapped to three external points of the octet Q=0. The vertexes (dd,ss,bb) are mapped to the combinations of singlet and octet "neutrals", the typical mix pi eta eta' in meson theory.

Can we get from here a specific characterisation of the "stop" pair of scalars? Not sure.

 

[arivero]

Updated v3 with a discussion of masses, https://arxiv.org/abs/2407.05397. Most koide related, but here the interesting thing is not the realistic but the "alpha=0" that provides pairs for everyone.

each particle in the (3,2) has one of the same mass when exchanging c<--->u
each particle in the (8,1) has an antiparticle in the (8,1) too.
The particles in the (6,1) come in pairs.

The selfenergies (or "masses") of the "preons" u,c,d,s,b are in this example 313,313,470,0,470. I think the model could be improved by including weak isospin.

 

[mitchell porter]

A natural counterpoint to these investigations can be found in the study of Seiberg dualities, which are really the modern version of preon theories. Recall that a Seiberg duality consists of a strongly coupled "electric" theory in the UV, and a "magnetic" theory in the IR containing weakly coupled states, which are actually bound states of the UV theory. The preons here are the fields in the UV.

Seiberg's original examples have N=1 supersymmetry in both the UV and the IR, but Sannino et al have written a number of papers in which the IR theory has supersymmetry, but the UV theory does not, though it may have a "gaugino" and/or "mesino" field. This may seem artificial, but I think this kind of non-susy theory can appear in string theory (see Armoni et al).

Sannino et al's latest, "Charting Standard Model Duality and its Signatures", came out this week. It shows the pros and the cons of such an approach. From our perspective, one downside is the multitude of extra fields. They are listed in table II. In the "magnetic" section, you can see that in addition to the SM fields (q, L, phi), there are "gaugino", "mesino", and "mes-Higgs" fields (lambda, M, phi_H).

Page 3 describes the series of effective theories interpolating between IR and UV:

Standard Model -> MSSM + extra superfields -> nonsusy dual + gaugino + mesino -> dual GUT

There are six flavors of dual quark in the UV, just as there are six flavors of quark in the IR standard model. One feature of this model, which could be an upside from our perspective, is that the UV chiral flavor symmetry SU(6)_L x SU(6)_R, gives rise to an IR flavor symmetry SU(3)_g x SU(2)_L x SU(2)_R, i.e. it includes a generation flavor symmetry *and* the chiral electroweak symmetry! (One of the missing pieces of the sbootstrap is how to obtain the latter.)

What about IR yukawas? Basically, in the second EFT above (the extended MSSM), there is a single yukawa, and a multitude of scalars in the "mes-Higgs" which have different VEVs, and the SM yukawas arise from the combination of these. The mes-Higgs is a UV meson composite of the UV gaugino and dual quarks (see equation 3), and the VEVs come from unknown operators in the far UV. After equation 10, they describe the couplings as "democratic", which should ring a bell for anyone who has studied the literature around Koide, but they don't actually explore that connection.

The reason I regard this as complementary to what @arivero is doing, is that it is an actual quantum field theory whose premises have some overlap with his. Sannino et al have an actual QFT but no hard numbers, just orders of magnitude. @arivero doesn't have a QFT, but a kind of susy preon idea, along with some simple mass formulas. The logical first step in bringing them even closer, would be to incorporate the "hadronic supersymmetry" and the "lepton-meson supersymmetry" of the standard model, into a Seiberg duality, rather than waiting for an entirely new supersymmetry to show up at the TeV scale.

 

[arivero]

The preprint about the sBoostrap from the point of view of SO(32) is now published as Eur. Phys. J. C 84, 1058 (2024). https://doi.org/10.1140/epjc/s10052-024-13368-3 if someone happens to need a reference some day.

It includes also some review of Koide, as I said before, but I will discuss it in the other thread.

My feeling is that it is equivalent to a classical Letter of Nuovo Cimento; the editorial process has been accelerated, they have labeled it as Letter and not Article, and surely the editor criteria has been the main weight for approval. In some sense it is correct because the EPJC was created as a fusion of multiple European journals including the particles section of Nuovo Cimento.

 

[mitchell porter]

Besides being a physical hypothesis, supersymmetry is also a formal tool that can be used in the study of non-supersymmetric theories. For example, there has been recent work by Murayama on using broken super-QCD to prove confinement and chiral symmetry breaking in various QCD-like theories. (I thought I posted about it here, but can't find it.) Basically, you describe the QCD-like theory as an SQCD in the limit where the superpartners become very heavy and drop out of the physics, but you make sure that the properties of interest, that can be proven for the SQCD, continue to hold in that limit.

Now there is another formal use of supersymmetry: "Field Space Geometry and Nonlinear Supersymmetry" by Yu-Tse Lee. The relevant concept here is that of "field redefinitions". I suppose an example of this from the standard model, can be seen in the shift between mass eigenstates and flavor eigenstates, in quarks and neutrinos. All the predictions (like scattering amplitudes) must be the same, however the fields are defined, and so field redefinitions reveal yet another aspect of physics in which there's a flexibility of description, independent of underlying physical realities.

There is a "field space geometry" for redefinitions of scalar fields and another for redefinitions of fermion fields, and the author is now combining these by embedding every scalar and fermion in a superfield. The price of this is to introduce fictitious superpartners, but these once again are formally treated as so massive that they can be neglected, Meanwhile, the author says,

"The supersymmetric extension of an effective field theory we constructed standardizes particles as superfields and packages Wilson coefficients as two potentials on the superfield space M"

From a sBootstrap perspective, what interests me is whether there is anything here that can fulfil the agenda in e.g. the last paragraph of #338. One motivation of the sBootstrap is these quasi-supersymmetries already implicit in the standard model and its effective theories; Lee's superfield space can take any theory made of scalars and fermions (equation 14) and extend it to an effective theory descended from something supersymmetric. What happens if we apply his method to the standard model and/or its effective theories, but we actually embed hadronic supersymmetry and lepton-meson supersymmetry?

Well, we can't really do it yet, since he hasn't incorporated gauge fields into his superspace method. But, gauge fields are being incorporated into the "field space geometry" approach (see references in Lee's section IV, on "the incorporation of gauge fields [into field space geometry] using vector multiplets". Presumably he sees, or hopes for, the extension of his own method via the inclusion of vector superfields.

 

[mitchell porter]

Mikhail Shifman, one of those great Russian physicists who moved to the west in the 1990s, has been an inspiration to me since the early days of this thread (see the final paper mentioned in #48). But today he's posted a paper

"QCD Chemistry: Remarks on Diquarks"

in which he says that heavy-light diquarks (containing one heavy and one light diquarks) "don't exist". That sounds bad for the sbootstrap! But what exactly does he mean? I think his proposition is, that at a certain energy scale, light diquarks become pointlike objects (page 7), whereas for example a "compact $bu$ diquark" never does (page 9). (And he says $cq$ diquarks lie on the borderline, page 10-11.)

In slightly more detail, his proposition is that light diquarks act pointlike at a scale which is about 9 times the QCD scale, with a mass similar to the mass of a single constituent quark, whereas the much greater current mass of the bottom quark dominates $bq$ dynamics, and drowns out whatever it is that happens with the ud diquark.

I think this is not a problem, if we suppose (as is repeatedly proposed in this thread) that diquarks are fundamentally open strings. It would just mean that the light diquark strings sometimes get into a zero-length regime, but the heavy diquark strings never do.

Just as a reality check, let me emphasize that there is no reference to supersymmetry in this paper (although Shifman has written plenty on that topic). This is purely an exercise in trying to develop heuristic nonperturbative models of quark behavior in the messy real world of heavy baryons.

What this suggests to me, is that there is an effective field theory for QCD, in which light diquarks can be treated as fields, while heavy diquarks could be modelled within a true string dual that exists at higher energies. From a sbootstrap perspective, perhaps the EFT can be approached via formal supersymmetric methods like those I mention in #340.

But what about hadronic supersymmetry for the heavy diquarks? As it turns out, there is a specific model for that, known as "superflavor" (e.g. Georgi & Wise 1990). This was originally devised for hadronic supersymmetries of the form baryon $Qqq$, meson $Q\bar{q}$, where $Q$ is a heavy quark and $q$ is always a light quark.

I did find superflavor being used in a Chinese paper (Jia et al 2014) about genuine supersymmetric phenomenology - instead of the meson $Q\bar{q}$, they have the supersymmetric baryon $\tilde{Q}\bar{q}$, where $\tilde{Q}$ is a heavy squark! It raises the question of how superflavor relates to the genuine, fundamental supersymmetry of their model; a question relevant to the sbootstrap if we do think that it is based on a fundamental supersymmetry and not just an emergent one. It wouldn't surprise me if there is some kind of duality here (as always, Seiberg duality comes to mind), with a light formal field-theoretic supersymmetry and a heavy emergent hadronic supersymmetry being two faces of some underlying super geometry.

 

[mitchell porter]

There is a preon model due to Bogdan Dobrescu

"A model of quark and lepton compositeness"

which has some similarity to the sBootstrap.

In the sBootstrap, we start with the five light quark flavors, we consider meson- and diquark-like pairings, and then superpartners of those, and (in theory) we get back all three generations, plus a handful of excess particles. And we often think of all this in terms of quarks on the opposite ends of a string.

In Dobrescu's preon model, he starts with fermionic preons that have standard model charges, and which also couple to a new strongly coupled preonic gauge group. Then, instead of binding them with string and looking at superpartners, he also adds another fermion in a "symmetric 2-tensor conjugate" representation of the preonic gauge groups.

The point of the analogy is that one model of a "fermionic string" is that it is a bound state of a quark, antiquark, and gluino. In Dobrescu, the 2-tensor fermion plays the role of the gluino. He ends up with "prebaryons" of the form

(preon with standard model charges + 2-tensor preon + preon with standard model charges)

with overall standard model charges that are just the sum of the standard model charges of the preons. And of course, that's how the combinatorics of the sBootstrap works!

First and perhaps most important, this gives us a new way to implement the combinatorics of the sBootstrap. Instead of a string with preon-quarks on the ends, we have a standard-model-singlet 2-tensor fermion which combines (thanks to the preonic gauge interaction) with two preon-quarks to form massless "prebaryons", among which are to be found the standard model fermions.

(Incidentally, this is not necessarily completely different from a string-based approach. See earlier comments about the work of Armoni, Shifman, and others.)

Second, it is of interest to grasp the specific combinatorics employed by Dobrescu. The sBootstrap starts with two up-type quarks and three down-type quarks (and all their antiparticles). Dobrescu starts with 15 fermion preons corresponding to the states of a standard model generation (without a right-handed neutrino), which he labels Q U D L E, and four more preons that are standard-model singlets. He then considers all possible pairings of these, as components of three-preon "prebaryons" where the third preon is the 2-tensor.

The results can be seen in his Table 2 (page 4), and are discussed starting at the bottom of page 3. An important part of his combinatorics, is that excess particles arise (beyond those needed for three generations), but they form vector pairs and are therefore presumed to acquire a superheavy Dirac mass.

This highlights another difference between Dobrescu's combinatorics and that of the sBootstrap, which is that he is working with chiral (Weyl) fermions and their hypercharge, whereas the sBootstrap is expressed in terms of Dirac fermions and their electric charge. From a fundamental point of view this is unsatisfactory, but we never quite found a clear model for a hypercharge sBootstrap. Well, Dobrescu shows us how it could be done, and one can consider e.g. a truncation of Dobrescu's QUDLE combinatorics, to see how much of the standard model he can get from his QUD preons alone (with or without the singlet preons too).

On the other hand, one can't just truncate Dobrescu's model, because of anomalies, and this leads us to some other features. His preonic gauge group is SU(15). That's actually what first caught my attention, since @arivero uses that group in his SO(32) paper. But @arivero is getting SU(3)_color x U(1)_em from his SU(15), along with the flavor symmetries SU(2)_up x SU(3) _down, whereas Dobrescu's SU(15) is completely separate from the standard model gauge groups.

Then there's the odd total of 19 preons in Dobrescu (not counting the 2-tensor fermion) - 15 corresponding to a single standard-model generation, and then 4 singlets. Regarding the 4 singlets, in a few places they serve the role of creating three prebaryons that correspond e.g. to three standard-model copies of a particular quark type, and then the fourth one forms a vector pair with an excess particles from elsewhere in the model. Also, the anomaly cancellations work out this way.

But we don't need to be too concerned with these details, except that Dobrescu has thereby given us a proof by example that this kind of model can work. The main question for me is, what happens if you try to embed sBootstrap combinatorics into a Dobrescu preon model?

 

[mitchell porter]

Craig Roberts has coauthored a large number of papers (most recently cited in this thread at #281 and #288) about the origins of hadronic mass. The latest such paper is

"Hadron Structure: Perspective and Insights" (Binosi, Roberts, Yao)

and it's quite dense with concepts and lore.

The authors distinguish between three contributions to mass generation: that due specifically to the Higgs boson (for hadrons, that basically means quark current mass); "emergent hadronic mass" which is a purely QCD effect (e.g. glueball mass would presumably be an example of this); and "HB+EHM", which is some kind of synergy between the two. The pion mass is an example of the latter - if the quarks were massless, the pion would be too (since they are Goldstone bosons of QCD's chiral symmetry). In reality they have a mass, but it is far more than the sum of their quark current masses.

On the other hand, consider the rho meson. It's just the spin-1 counterpart of the pion, but it has a mass which is 2/3rds of the way to the nucleon mass. I don't think Roberts et al explicitly say this, but the rho mass is basically equal to the pion mass plus two constituent quark masses. What they do say is that the rho, like the nucleon but unlike the pion, is a particle whose mass is dominated by the purely-QCD mechanism, whatever it is. (On page 2 they seem to say that two classic hadron mass formulas, Goldberger-Treiman and Gell-Mann-Oakes-Renner, explain a lot of this.)

Interestingly, they also mention the similarity between the muon and pion masses. But they don't say anything as wild as suggesting that supersymmetry is somehow involved (the closest thing to a model for that might be the Polchinski-Strassler paper mentioned here in #265).

On page 8, they may be giving a theory of the origin of the constituent quark mass. They mention a momentum-dependent running mass for light quarks which becomes approximately 350 MeV at zero momentum. Diquarks are mentioned in the context of the quark+diquark approximation of the baryon, but one should see Roberts's earlier works for the details of diquark masses.

These papers are just studying mechanisms of hadronic mass. But for those of us interested in the sBootstrap and in Brannen-Koide mass formulas, we should be interested e.g. in stringy and supersymmetric generalizations. As far as the strings are concerned, I would like to see whether counterparts of EHM and HB+EHM can be found in stringy models of QCD like Sakai-Sugimoto.

As for trying to bring in the leptons... If you look at the mass scales, it's as if the electron mass is at the "purely HB" mass scale (in that its mass is comparable to the current masses of the light quarks), the muon mass is at the HB+EHM scale (since it's around the pion mass), and tau mass is closest to the "purely EHM" scale (being greater than the nucleon mass).

It's a weird comparison to make because the standard model tells us that the charged leptons all get their masses via the same mechanism, "HB" - it's just the yukawa couplings that differ in magnitude. In a beyond-standard-model theory, it's not necessarily so simple - e.g. there can be systematic differences in how the different generations get their masses.

But here, we're looking at the idea that the leptons are quasi-goldstone fermions. And not just that - there are a number of BSM models in which all the standard model fermions are quasi-goldstones, but I think it's normally supposed that they are all fundamentally massless (i.e. superpartners to exactly massless pion-like particles, see #327), and then get all their mass via a Higgs interaction. Here we are asking whether there are contributions to lepton mass, that are super-QCD counterparts of "EHM" and "HB+EHM".

Furthermore, if we also want Koide's formula to result from a mechanism rather than a coincidence, we really need the super-QCD explanation of charged lepton masses to be the same for all three (in some sense)... If the charged leptons were all fundamentally massless quasi-goldstones, and the Higgs a top-pion (as it is in topcolor theories), you could try to directly mimic the SM Higgs mechanism in your underlying super-QCD theory... On the other hand, Martin Schumacher had some papers arguing that a version of the Higgs mechanism is responsible for baryon mass, with the sigma meson as the counterpart of the Higgs, and (I think) the pion condensate as the counterpart of the Higgs VEV. It seemed a bit too glib to be true, but he is actually building on ideas from Schwinger which are also part of the ancestry of the actual Higgs mechanism... Maybe there could be a Seiberg-dual perspective on standard model Higgs couplings, in which they become Roberts-Schumacher interactions in an underlying super-QCD theory, with an "EHM" contribution as well as an "HB" contribution.

 

[mitchell porter]

A comment on something that may or may not be a digression: I have just had my mind blown by learning, twenty years late, the gist of the "Dijkgraaf-Vafa correspondence". To begin with, it helps if you are familiar with the idea of color branes and flavor branes, with a string between color branes being a gluon (or gauge bosons), and a string between a color brane and a flavor brane being a quark (or fermion charged under a gauge field). Since this is string theory, usually there is some supersymmetry, and so these strings actually represent gluon-gluino and quark-squark superfields, respectively.

Now consider a Calabi-Yau manifold (the extra compact dimensions) with color branes wrapped around a "cycle" (topologist's jargon for a "hole", like the hole in a donut). As mentioned, the open strings between the color branes correspond (at the level of field theory) to gluon-gluino superfields. The branes are also capable of oscillating in directions normal to the cycle; these displacements are scalar quantities, and correspond to "chiral superfields" at the level of field theory (with a scalar and a spin-1/2 component).

It turns out that in string theory, there is a dual perspective available (very similar to AdS/CFT) in which the picture of "branes wrapped on a cycle" is replaced by "flux passing through dual cycles". The strings in the brane picture were open strings ending on the branes. In the dual picture, there are no more branes, so only closed strings are possible and they make up the flux. The flux actually corresponds to certain generalized charges that the branes possessed; so even though the branes aren't present in the dual picture, all their physical effects are.

The amazing thing is that the flux encodes information about composite objects in the field theory! The main superfields arising from the color branes were gluon-gluino superfields, and the fluxes tell us about gluino-pair condensates and glueballs made of gluons. They are closed-string objects made of webs of open strings.

It was amazing enough to be grasping this vision, but even more so that I was instructed in it by an AI (OpenAI's 4o model, so not even their more advanced 4.5 model). You can see the conversation here. I had been studying the actual papers, but there were basic questions for which I wasn't finding the answers, and the AI was able to answer them, and other questions that arose, with what I think was amazing flair.

In any case, having grasped how the glueballs and gluino condensates were represented by fluxes dual to the branes, I wanted to know about mesons and baryons - do they have a place in Dijkgraaf and Vafa's correspondence? At this point we need to introduce some flavor branes. It turns out that the flavor branes are the same on both sides of the duality. It doesn't sound that different to the way that holographic QCD (Sakai-Sugimoto) usually works. Mesons are quark-antiquark strings, so they are open strings among the flavor branes only, and baryons are branes wrapped around the dual cycles that emerge on the flux side of the duality (and connected by quark-like strings to the flavor branes).

Perhaps the most interesting thing here, is that this is also a picture of confinement. Confinement means that colored degrees of freedom become invisible; in stringy terms, this means that there are no color branes in the flux picture, just flavor branes, condensates, and composite objects. It's a remarkably thorough mapping of the phenomena of strongly coupled gauge theory, into string theory... But, it's supersymmetric, so if you want to understand QCD this way, you'll still need something more (again, something like Sakai-Sugimoto, which breaks the final supersymmetry).

However, in the sBootstrap, we have a supersymmetry, so what I wanted to know is, is Dijkgraaf-Vafa useful here at all? So far, I haven't made a connection. In fact, even though so much N=1 supersymmetric phenomenology has been studied over the years, I haven't found applications of Dijkgraaf-Vafa to phenomenology in general. I tried looking for something involving yukawa couplings, and found this paper, but didn't get anything from it yet. The paper piqued my interest because it talked about theories with an adjoint (the gluino) and several quarks, and reminded me of Armoni's work on "orientifold planar equivalence", cited a few times in this thread. I keep wondering e.g. if the diquark could be represented as a "flavino" fermionic string between flavor branes; but then it seems we want that for mesinos, which in the sBootstrap is where the leptons come from. It could be that Dijkgraaf-Vafa is from the realm of color, and the sBootstrap is from the realm of flavor, so they just don't have much to do with each other.

edit: I completely forgot to mention another aspect of the Dijkgraaf-Vafa correspondence, which is the role of "matrix models". This is a kind of noncommutative geometry, I guess, in which you literally do integrals over possible values of matrices, in order to recover open strings in a space-time. The key is to interpret the row and column numbers of the matrix as identifying particular branes. Matrix element (i,j) then corresponds to a string between brane i and brane j. The equations for a matrix model involve matrix-valued quantities, and determine the interactions among strings in the same way that you get Feynman rules from an ordinary Lagrangian. The more algebraic part of the Dijkgraaf-Vafa correspondence involves showing how the matrix model algebra is still present, even when you only have closed strings...

Phenomenologically, the matrix model that interests me most is the "IKKT model", a Japanese matrix model which has intrigued a minority of researchers for many years, and which has just had a renaissance - I give my take on it here. I think that technically it has some differences with the matrix models studied in Dijkgraaf-Vafa (for example, time is supposed to be emergent in it, as well as space!), but having understood the Dijkgraaf-Vafa path from matrix model to open strings to gauge theory and closed strings, it wouldn't hurt to look at it from that perspective too.

 

[mitchell porter]

Via Tommaso Dorigo, I have just learned of a possible observation of toponium (top-antitop meson) at CERN's big muon detector (CMS experiment). This interests me because I've always been keen on the idea that the Higgs boson could be a kind of toponium (the Higgs mass is basically 1/sqrt(2) times the top mass). But it also matters for the sBootstrap, because one of the premises of the sBootstrap is that you only use the five light quarks (light relative to the top quark, that is - usually bottom and charm aren't counted as light) as ingredients in the mesons and diquarks whose superpartners are all the standard model fermions.

I shall see what @arivero himself thinks, but in my opinion the existence of a toponium resonance is not inherently a problem for the sBootstrap. For example, in an interpretation of the sBootstrap as a Seiberg duality, it's not that there aren't six fundamental flavors of quark (only having five leads to problems with anomalies), but rather e.g. that one is massive and five are massless in the UV, while their IR duals are the sBootstrap composites and exhibit the familiar spectrum of masses.

There would still be the question of whether toponium has a superpartner (remember, one of the sBootstrap ideas is that the leptons are superpartners of mesons) - if so, where is it, and if not, why not. One perspective on this, is that it is a form of the general question, what about all the superpartners that ought to exist, but for which the sBootstrap doesn't have a use. This applies to the charge +4/3 "diquarkino" arising as the superpartner of a diquark made of two up-type quarks - a fermion with such a charge may actually exist in certain SUSY GUTs, as the spin-1/2 partner of an X boson. But it also applies to the superpartners of all the elementary bosons - photino, gluino, Wino and Zino, and higgsino.

If you're not worried about being an old-fashioned SUSY phenomenologist, you can just approach this in the spirit of the usual MSSM - these particles are out there, they're just heavy. But this kind of SUSY is a little out of fashion these days, at least in some circles. Part of the charm of the sBootstrap is that it gives SUSY an unexpected phenomenological role within the standard model (similar in spirit to the early days of SUSY phenomenology, when it was wondered if the photino might just be the neutrino). So one has a choice of approaching the sBootstrap as a kind of extra emergent SUSY embedded in the MSSM, or as a kind of partial SUSY existing within the non-SUSY standard model.

Anyway returning to CMS's "pseudoscalar excess" that might be toponium, in their paper they do say that alternative explanations are presently possible, and cite this earlier CERN preprint, in which they cover the possibility of a two-Higgs model. I also just wonder how confident we are in the modeling of top-antitop interactions, since the top and the Higgs are strongly coupled (because the top yukawa is so big). I was curious about this back in the days of the "750 GeV diphoton excess", for those who remember that...

 

[arivero]

Indeed I am a bit worried, lets see if they find some discrepancy with models.

 

[mitchell porter]

Their most recent reference (December 2024) for the calculation says

"Green's functions ... are obtained from the solution of a Schrödinger equation accounting for the exchange of potential gluons among the top and anti-top quark ... the ttbar pair transition into a quasi-bound state is favored. This state is colloquially referred to as ‘toponium’, although it should be noted that the top quark decays much faster than it can hadronize, i.e. Γ_t ≫ Λ_QCD, and thus a proper bound state cannot form, unlike the more common charmonia and bottomonia."

So there appears to be an objective difference. How that difference manifests will depend on the formalism or approximation being used. It would be especially interesting to know what the difference amounts to, in nonperturbative QCD, and in a fully string-theoretic framework.