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

Gold Member
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.

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

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.

arivero
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?

arivero and ohwilleke
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.

Gold Member
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.

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 and arivero
ohwilleke
Gold Member
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.

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ohwilleke
Gold Member
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.

Gold Member
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
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."

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Gold Member
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.

ohwilleke
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.)

arivero