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

1. Jul 31, 2013

### mitchell porter

I have looked more closely at papers by Cabo (comment #186) and have mixed news. There were some impressive-looking tables of predicted masses in early papers, but it turned out that these were still assuming the usual current masses; the tables just showed the pole mass for the proposed modified quark propagator, which was basically the same as the Lagrangian mass for heavy quarks, but close to the constituent mass for light quarks. The use of a "democratic" ansatz only managed to produce a heavy top and heavy bottom and everything else massless, which might be OK for a first step, but it's still far from a cascade of Koide triplets...

However, the most recent paper in this program managed to predict a mass-generating scalar of mass 126 GeV! I do not understand how it was done, and even the author writes of wanting to get the mass closer to 114 GeV, where there had been a spurious Higgs sighting. It's always interesting when the theory knows better than its creator...

The theoretical difference between this modified perturbative QCD, and the usual sort, seems to be the presence of gluons in the asymptotic states. So these are quark propagators dressed by a gluon condensate. This aspect of the work (as opposed to the idea of predicting quark masses) was taken up by another physicist, Paul Hoyer, and Hoyer's work was cited e.g. in a QCD review by Chris Quigg in 2011...

I think one might want to view this - I mean the full program of obtaining quark masses from QCD plus condensates - as a type of bootstrap approach, in the 1960s sense. As Ron Maimon points out, string theory came from the bootstrap, so it's conceivable that "SM from bootstrap" leads also to a type of string theory...

Something which I do find lacking in the Cabo papers so far, is anything to do with the weak interaction, and especially the combination of left-handed weak doublets with right-handed weak singlets, which are crucial to the generation of mass in the SM. I have no idea how to make a chiral gauge theory "emergent" from a "bootstrap".

edit: I've had a closer look at the "126 GeV" paper. Version 1 dates from June 2010 and "predicts" a scalar field with a mass of 113 GeV. Version 2 dates from February 2011, and "predicts" 126 GeV. The different "predictions" are obtained by varying a scale parameter μ in a way that I do not see explained. It's just, "let's consider what happens for this value of μ, no wait, let's consider this other value of μ". And February 2011 is getting close in time to the observation of the Higgs - though even as early as 2007, there were estimates (page 2 here) based on electroweak measurements, which put the central value of the Higgs mass at 129 GeV, but with large uncertainties - so perhaps one can't presume that version 2 was motivated by inside information.

Last edited: Jul 31, 2013
2. Aug 2, 2013

### mitchell porter

Today, two SQCD papers, mostly from Japan:

1) "Quark confinement via magnetic color-flavor locking" by Kitano and Yokoi. Kitano has featured previously in this thread (#111, #148, #172). Color-flavor locking has also made an appearance (#73, #161), as has "hidden local symmetry" (#48 first edit, #111, #126), a theme of this paper.

If strong dynamics is capable of explaining the relationships we have just been discussing, this is very much how I envisage it working: color-flavor locking in the "magnetic" theory of a Seiberg duality, producing dual "electric" quarks at lower energies... In other models of CFL, it happens through diquark condensates... It's exciting to see the slow advances here.

2) "Dynamical Supersymmetry Breaking with T_N Theory". The only author I recognize here is Yuji Tachikawa, who is the "T" in the "AGT" relation, a connection between d=2 and d=4 theories that has received lots of high-powered theoretical attention. He comments occasionally in forums like Math Overflow... This paper offers a model of susy-breaking in SQCD coupled to an exotic superconformal sector. Its relevance is a lot more tenuous, but conformal sectors and conformal symmetries are showing up a lot in BSM theory these days; in this thread, see #49, #55, #143, #180.

3. Aug 5, 2013

### MTd2

http://arxiv.org/abs/1308.0402

Critical String In (3+1)+4 Dimensions
J.S. Bhattacharyya
(Submitted on 2 Aug 2013)
We assume that a string moves in an eight dimensional space that can be divided into the physical four dimensional Minkowski space and a four dimensional Euclidean internal space (we call it so) that can be identified with gauge symmetries and there are two N=1 local supersymmetries on the world-sheet, one applicable to the world-sheet bosons and fermions belonging to the physical space as in the NSR model and the other to those belonging to the internal space at the classical level. We use canonical method to calculate Virasoro anomaly. We anti-normal order the contributions of the physical fermions (not fermionic ghosts) to the Virasoro algebra. This changes sign of their contributions to the Virasoro anomaly and shows that critical strings can exist in four dimensional physical Minkowski space. It yields a spectrum very similar to the $N=1,D=10$ theory, but with some differences. The ground state in the fermionic sector of open strings is a Dirac spinor in this case. The Standard Model turns out the most natural choice of gauge symmetries, if the number of generations is three.

4. Aug 5, 2013

### mitchell porter

There's a type of string called a "parafermionic string" where the fermions don't have the usual statistics, and this can be used to get the critical dimension down to 3+1. Here's a recent example which also claims to get three generations. I don't know how it relates to the familiar string synthesis, but presumably it makes some mathematical sense, since some big names have been involved.

I can't say the same for Bhattacharyya's paper. The starting point - let's "anti-normal-order" the fermions, rather than normal-ordering them - at least looks like an idea of some substance, that would be mathematically nontrivial to explore. But the later steps (an extra "Euclidean" internal space, the two "supersymmetries") look like they are being introduced in a very slapdash way, which increases the odds that the ideas are trivially inconsistent as described - inconsistent for elementary reasons.

... though not so elementary that I can tell you exactly what the problem is, unfortunately. :-) I still have a few gaps in my stringy basics, and don't have the time right now to fill those gaps, and make a precise critique. But the other paper may be a better example of how to carry out the same intention, of an SM-like string theory from parastatistics.

5. Aug 5, 2013

### MTd2

Isn't there a way to do string without determined signature or statistics, where criticality is just a sort of "on shell" condition?

6. Aug 5, 2013

### mitchell porter

Maybe? There are papers from '92-'93 by Myers and Periwal which talk about how going off-shell is related to non-criticality, and around the same time Witten start to define string field theory on a "space of all worldsheet theories". I don't know where it led.

7. Aug 5, 2013

8. Aug 9, 2013

### linasv

Skyrmions

Kind-of off-topic, but one old and curious model for the baryon was the Skyrmion: a topological soliton in the pion field. That, and its extension to a "chiral bag model" (quarks on the inside) hints at a certain duality between mesons and quarks. (The model is interesting because it gets the baryon mass, magnetic moment right, given only one input: the baryon radius). I can't help but think of this when I hear "hadronic SUSY".

As far as I know, these models have had very little elaboration or theoretical attention, although Dan Freed (at UTexas/Austin) did manage to place the whole affair on a far stronger mathematical footing, circa 2005 or so. Specifically, I think (not sure) he showed that the topological soliton really does have spin-1/2 statistics; and that its a SUSY dual; or something like that. I don't recall if he needed strings to do this. (it was already known long ago that the topological winding number is the baryon number).

9. Aug 21, 2013

### mitchell porter

Sorry for the delayed reply, also apologies for a curt tone in what follows, I just had a browser crash wipe out a longer answer...

At inspirehep.net, there are over a thousand papers about skyrmions listed. Some are recent and about holographic QCD, the modern mainstream approach to getting QCD from string theory. So the topic is well-known, it's just a question of how it relates to everything else in QCD.

The most relevant 2005 paper from Dan Freed that I can see is "Pions and Generalized Cohomology", which is deep and vaguely in the same territory, but not explicitly about skyrmions and otherwise not as you describe. Were you thinking of someone else?

I am also reminded of "Geometric Models of Matter" by Atiyah et al, which is Skyrme-like, and which PF seems to have overlooked so far - surprising, since such attempts to get the standard model from simple geometric or algebraic constructions tend to generate at least one thread here. And Atiyah is a very big name in math.

This week also brought another paper by a Russian physicist who has long claimed that he can get mesons and baryons from a modified approach to string theory. Like the paper by Bhattacharya discussed earlier (#203), it is certainly "fringe" from a mainstream string perspective and I would guess that it is wrong in certain technical particulars... meaning it is right at home on this thread, which is all about a lopsided alternation between dubiously ambitious "what-if"s, and more conservative work with better bonafides.

10. Jan 5, 2015

### mitchell porter

11. Jan 26, 2016

### mitchell porter

I was briefly excited today, when 2/3 of the authors of the paper above, came out with another, connecting the important κ parameter of their model to the mass of the proton (see top of page 3). But just a few pages later (middle of page 7) they want to use a different value, connected instead to the rho meson. And in a review paper also released today, one of the authors seems to use (page 14) yet another value of κ. So they are still messing with their theory. But I thought it worthwhile to note how their model connects with concrete QCD scales.

12. Jan 30, 2016

### arivero

They still need to get courage enough to try to bit the lowest state of the fermion regge trajectory to a quark :-)

13. Mar 29, 2016

### mitchell porter

Well, here's the problem. You can observe the higher states on the regge trajectories for some hadrons. And orthodox string theory does imply that there are regge trajectories for the SM fermions - but the higher states start unobservably high, at the string scale. So the two string regimes shouldn't have much to do with each other. And on the other hand, if we suppose that SM fermions are somehow peers of QCD hadrons, in a new version of Chew's nuclear democracy, why haven't we seen their excited states too?

Nonetheless, I was interested today to run across the talk "Quark-Hadron Duality in Electron-Pion Scattering". It starts with two dualities, the Dolen-Horn-Schmidt duality that inspired dual resonance theories prior to the standard model, and the Bloom-Gilman or quark-hadron duality which came later, and which seems to be about interpolating between perturbative and non-perturbative QCD. The dualities are then given a purely QCD explanation (slide 6), in terms of the operator product expansion.

One idea that I have derived from the sBootstrap, is that the fundamental theory could be a type of SQCD, with leptons and electroweak sector arising from mesinos and Seiberg duality. So now I'm wondering, could the SQCD counterparts of the OPE - and the sum rules and non-perturbative techniques and all the other methods of advanced QCD - be the key to taking all of this another step further.

14. Jun 10, 2016

### mitchell porter

In a paper on tetraquarks, Sonnenschein and Weissman employ a particular stringy model of a diquark, as two nearby quarks joined by short strings to a "baryonic vertex", to which a third quark is attached by a longer string. See figure 3, bottom of page 8. u, s, c are flavor branes. A meson is an open string directly connecting two flavor branes (or two points on the same flavor brane). The baryonic vertex is actually a localized brane wrapping compact dimensions, and a baryon consists of quark strings running from flavor branes to this baryonic brane. That is an old idea; what Sonnenschein and Weissman add, is the idea that two of the quark strings are really short, forming an effective diquark. A baryon would then be a quark-diquark string with a baryonic vertex at one end. This quark-diquark string can itself rotate and has excited states forming a Regge trajectory.

The sBootstrap concept of lepton-meson supersymmetry can still work within such a model if the meson string is a superstring. But it's much less clear to me how, or whether, quark-diquark supersymmetry can work. Mesons here are strings and their mesino superpartners are strings too, but a diquark here isn't a string, it's just 2/3rds of a baryon. A diquark in field theory isn't even a gauge-invariant object (and that's problematic), and that probably translates to S&W's stringy diquarks in some way. Still, even if there isn't something as straightforward as a "diquarkino string", there might be a "fermionic diquark operator" in a superstring implementation of this model, with a similarity to an antiquark.

15. Jun 10, 2016

### arivero

It is particularly disturbing that they use the example cu, with the damned charge 4/3.

16. Jun 15, 2016

### mitchell porter

Current thoughts on this: First, charge 4/3 diquarks in themselves are not a problem. Like the other diquarks, if they exist, they occur inside baryons. The problem is the charge 4/3 "fermionic diquark" or "diquarkino" - that's the thing which is not seen, and which spoils the mapping between quarks and diquarks.

One idea I like, is that charge 4/3 fermionic diquarks form a neutral condensate. It would perhaps be similar to a tetraquark condensate or a diquark-antidiquark condensate. It doesn't really explain why they don't show up as exotic "quarks", i.e. as components of exotic baryons, but at least it gives them something to do.

More generally speaking, an extension of Sonnenschein and Weissman's "holography-inspired stringy hadrons" to include supersymmetry and charged quarks, sounds like a framework where you could implement the sBootstrap, and actually just calculate the consequences! It would be a miracle if it did produce the standard model, but even without a miracle, that would still be a huge leap forward.

Unfortunately their framework still seems to be very preliminary. However, today has already yielded arXiv:1606.04111, a study of tetraquark condensates for two and three light flavors (complete with intriguing mass formulas in section V). So I am optimistic again, that a dynamical toy model of the sBootstrap can and will be constructed.

17. Jun 15, 2016

### arivero

I would also enjoy a sort of "neutral condensate" solution to hide the 4/3 diquarkino.. but lets wait some months and see if Strassler's ambulance-chasing has happened to hit the jackpot

http://arxiv.org/abs/1602.08819
Resonances from QCD bound states and the 750 GeV diphoton excess
Yevgeny Kats, Matthew J. Strassler
(Submitted on 29 Feb 2016 (v1), last revised 13 May 2016 (this version, v2))

"We find that the recently reported diphoton excesses near 750 GeV could indeed be due to a bound state of this kind. A narrow resonance of the correct size could be obtained for a color-triplet scalar with electric charge -4/3 and mass near 375 GeV, if (as a recent lattice computation suggests) the wave function at the origin is somewhat larger than anticipated. Pair production of this particle could have evaded detection up to now. Other candidates may include a triplet scalar of charge 5/3, a triplet fermion of charge -4/3, and perhaps a sextet scalar of charge -2/3."

18. Jun 15, 2016

### arivero

19. Aug 28, 2016

### mitchell porter

A paper today, "Mass Ansatze for the standard model fermions from a composite perspective", proposes an unusual preon model with the following similarities to the sBootstrap: the preons have hypercharges like the SM quarks; the confining interaction is QCD. The preons transform under a reducible representation of SU(3) color, 3* x 3*. The mass formulas proposed are based on the Gell-Mann-Oakes-Renner relation. There is no mention of supersymmetry, though one of the authors (Renata Jora) wrote a heterodox MSSM paper once... The use of product representations for preons reminds me of work by Adi Armoni on k-strings and orientifold equivalence.

20. Mar 14, 2017

### mitchell porter

Another formalism that would be relevant: chiral perturbation theory extended to include diquarks and supersymmetry. One might start by constructing a non-supersymmetric theory of mesons and diquarks, treated as elementary fields in the appropriate flavor representations. Then, add supersymmetry. According to the sBootstrap, the "leptons" and "quarks" will now appear as the superpartners! - a humorous reversal of the usual relationship.

There is already an extension of chiral perturbation theory to include heavy quarks and diquarks, which employs superfields to represent a heavy quark-diquark symmetry found by Savage and Wise (http://www.researchgate.net/publication/222490324_Spectrum_of_baryons_with_two_heavy_quarks [Broken]). (Incidentally, the Savage-Wise construction has a U(5) symmetry which they call "superflavor".) There is also a supersymmetric extension of chiral perturbation theory in which the pions have "piino" superpartners. Could the combination of these two formalisms arise in some limit of SQCD?

edit: I have remarked before that the very existence of the "diquarkino" or "fermionic diquark" is a problem, because the diquark is not a gauge-invariant object. However, it is such in SU(2)color QCD, and Shifman and Vainshtein say that there should be a sort of continuity of properties connecting the SU(2)color diquark and the SU(3)color diquark. But the SU(2)color diquark should have a genuine superpartner in SU(2) SQCD; which makes me think that there really may be a diquarkino in SU(3) SQCD, perhaps of the form $qλq$, where $λ$ is the gluino, or $q \tilde{q}$, where $\tilde{q}$ is the squark.

Last edited by a moderator: May 8, 2017