
#127
Feb2412, 07:05 PM

P: 748

I have kept thinking about how this could work in conjunction with the Koide relations for quarks. Sevral ideas:
1) The flavor symmetry of the sBootstrap, if gauged, could be the Sumino family symmetry that protects the Koide relations. 2) Get the GUT group and the gauged family symmetry group from an extra dimension, possibly deconstructed. 3) The overall theory is a supersymmetric extended technicolor theory in which the techniquarks are the electric quarks of a Seiberg duality. The magnetic theory is to be a KoideSumino model in which the yukawas come from flavon VEVs  but the flavons are actually condensates from the electric theory. 



#128
Feb2512, 07:11 PM

PF Gold
P: 2,885

It could be better to think not of the flavour symmetry of "the sBootstrap" but of the "flavour symmetry of the scalar sector of susy", or even of the "composite flavour symmetry", because it is always 5x5 and a 5x5+5x5. This fact is independent of the sBootstrap hypothesis and in this way it could be more palatable.
Just in case that some newcomer reaches this thread, let me reminder that S(5x5) is a 24, for the sleptons, and that, with some abuse of notation, S(5x5+5x5) is a 30, from which a 24 are the usual squarks of a given colour charge, and the extant 6 are the problematic, or intriguing, + 4/3 scalar pests. 



#129
Feb2712, 04:47 AM

PF Gold
P: 2,885





#130
Mar1112, 10:41 PM

P: 748

Two papers today which fit the agenda of comment #127 (points 1 and 3): "Family Gauge Bosons with an Inverted Mass Hierarchy" and "Scalar Mesons in Holographic Walking Technicolor". The first paper, coauthored by Koide, adapts the Sumino mechanism to a supersymmetric theory. The second paper looks at the spectrum of composite scalars in a strongly coupled supersymmetric technicolor theory  so it's relevant for understanding how a theory like that in the first paper (which accounts for Koidelike relationships among particle masses by positing a set of scalar "flavons" or "yukawaons") could emerge from a sBootstraplike model.




#131
Mar2112, 04:08 AM

P: 748

Looking back over a year of speculation in this thread, I am alarmed by how little I really knew about the topics under discussion (e.g. standard model, supersymmetry). I don't think I said many false things, but I was really flying blind a lot of the time. I say this because, having attained to some relatively sober and at least superficially plausible ideas in recent comments, I want to sketch another bigpicture approach, and that means a return to going far beyond what I know about.
I'll start with Strassler's review of Seiberg duality. I have thought for a long time that the case of interest for the sBootstrap is SQCD, with Nc = 3 colors and Nf = 6 flavors, and N=1 or 2 supersymmetry. The N=2 case is selfdual; the N=1 case has a dual which also has 3 colors and 6 flavors, but in addition there is a new meson superfield. For the sBootstrap to work, the quarks have to have the appropriate charges. So we might imagine the N=2 case with an extra U(1) gauged. Also, we give the top a large mass while keeping all the others massless (because the sBootstrap involves the combinatorics of five quarks, not six). Let us suppose we have gone from N=2 to N=1 supersymmetry along the way. Now suppose we take the Seiberg dual of this N=1 theory. The idea is that the leptons will emerge as part of the meson superfield, and the other five quarks will also acquire nonzero masses in the dual picture. This picture is missing certain details. How exactly is supersymmetry broken? Where do weak interactions and parity violation come from? What about the Higgs? In recent comments I've speculated about getting scalars (Higgses, flavons) from composites. It may be possible to break an N=2 theory to get parity violation, but apparently it's challenging to do so in a way consistent with experiment. The origin of fermion masses has to be more complicated than in the standard model because the usual massgenerating terms don't exist. Without having shown that any of this really can work, I now want to add two further speculations to the mix. First, Alejandro has pointed out that the top quark Yukawa is unnaturally close to 1. It's not just of order 1, which would be technically natural; it's within less than 1% of being exactly 1. In my recent response to his observation (see preceding link), I've outlined the barest beginnings of a strategy for explaining this observation, in the light of new calculations by Rodejohann and Zhang. This could be added as a further epicycle on the "3color, 6flavor" approach to the sBootstrap that I just outlined (according to which there is a Seiberg duality, on one side of which the top Yukawa is "large" and the other Yukawas are zero, and on the other side of which is the standard model, with all quark Yukawas nonzero). Second, way back in comment #110 (page 7) I mentioned that N=2 Nc=3 Nf=6 SQCD (with all quarks massless) has a twistorstring representation. The twistor space employed to define this twistor string with flavor is very similar to the one used by Witten in his 2003 paper, it just has slightly different branes and boundary conditions. What I would like to know is whether one can reproduce Heckman and Verlinde's recent construction using hits twistor space, in order to produce the N=2 theory coupled to gravity in a cosmologically realistic space. It's just an idea about what the ultimate context of a "3color 6flavor sBootstrap" might be. Finally, I have to wonder if some version of my "N=8 cosmology" could apply here. The idea there is to take a particular AdS4/CFT3 model with an impressionistic resemblance to reality, and then to use gravitino condensates to uplift it to positive spatial curvature. The model in question has an SU(3) x U(1) local symmetry, and under SU(3), the eight gravitinos of d=4 maximal supergravity form a triplet, an antitriplet, and two singlets. The idea is that the triplets are the dark energy and the singlets are the dark matter... The "N=2 sBootstrap" above also has SU(3) x U(1) symmetry (the U(1) gives the quarks the charges needed for the sBootstrap combinatorics), so one might hope that an embedding in Mtheory could produce the desired gravitino spectrum. The N=8 cosmology starts from a perturbed version of ABJM theory, while the twistor string (in its unflavored version) gives rise to N=4 YangMills, and there are deep relationships between ABJM (an N=6 theory) and N=4 YM, but they're too deep for me to say anything sensible about how they might relate to this project. The most plausible conclusion of all might be that the theory we're looking for is to be obtained from a string theory construction of conventional intricacy (e.g. compactification on a CalabiYau of the sort that phenomenologists already study), and everything I've just discussed is still too simple  though it might be a step towards the real thing. 



#132
Apr712, 11:36 AM

P: 748

Way back in comment #47 (on page 3), when I was still figuring out the difference between a QCD diquark and a GUT diquark, I mentioned a paper from 1990, "Radiative generation of quark and lepton mass hierarchies from a topquark mass seed" (free copy). I just revisited it, and I am amazed by how many of the properties you're looking for are satisfied by their model.
What took me back to it was the search for an explanation of the chained Koide triplets among the quarks. The Koide triplet for leptons relates corresponding particles in different generations, and this is much friendlier to standard thinking than the sequential quark triplets tbc, bcs,... Eventually I thought to look for models in which all the fermion masses descend from the top, via loop effects. And then I noticed that in the paper above, "We show that the simplest model one can construct has the following cascade: tree level>top; one loop>bottom; two loop>charm, tau; three loop>strange, mu, up, down; four loop>electron." Now suppose for a moment that in some model of this type, masses arising at n, n+1, and n+2 loops (for certain values of n) naturally satisfy the Koide formula for some reason. Then right away not only do we have the tbc, bcs, and taumue triplets, but tau and mu are also correctly "aligned" with charm and strange, for e.g. a GeorgiJarlskog explanation of the factor of 3 relating their "Brannen" parameters. Something goes a little wrong with up and down, but their masses show the greatest deviation from the chained Koide ansatz anyway. The radiative generation of masses is accomplished by having scalar diquarks and scalar leptoquarks which can change the particle species and allow alreadymassive particles like the top to appear in a loop. (Also one needs a Z3 symmetry to prevent particles other than the top from picking up treelevel masses via the usual couplings to the Higgs.) The couplings of these new scalars are arbitrary; the form of the model is constrained only by the requirement that the rank of the mass matrices grows appropriately, as higherloop corrections are added. So there is no immediate explanation of Koide formulae here; but that's not a problem. This is really a representative of a whole class of models, and what one should now do is search the class for a specific model in which Koide relations appear. 



#133
Apr712, 02:44 PM

PF Gold
P: 2,885

Mitchell, let me note that Volkas is still working on diquarks and he lives near your home, so perhaps some friend or even yourself could happen to have attended some lecture of his? 



#134
Apr712, 03:07 PM

PF Gold
P: 2,885

The problem is, really, that the diquark idea and Koide cascade have still not evidence for a connection. Koide was the motivation for diquarks because Koide model were more easy to understand from compositeness, as in the original papers. But the sBootstrap is not connected (yet?) to Koide cascade.




#135
Apr812, 02:12 PM

PF Gold
P: 2,885

Really it would be a real shock if the MSSM sfermion content (which is the one we produce in the sBootstrap) with some extra interaction were able to generate the mass spectrum of the standard model, and in the Koide format. That should be beyond coincidence.




#136
Apr912, 11:46 AM

P: 748

Other work by Foot suggests an interpretation of the mirror fermions appearing in the N=2 Nc=3 Nf=6 theory: they make up the dark sector! I just found this in Sheppeard's "ribbon dark sector" paper, which ends with some numerology connecting Koide phase parameters, dark sector fractions, and quarklepton complementarity. Foot wrote a whole book arguing that dark matter is mirror matter... So maybe it's time to unearth Nir Polonsky's papers on N=2 phenomenology, and see if we can't get a Koide cascade and emergent leptons in the visible sector, and everything dark in a mirror sector.
I don't think I ever saw Volkas or Foot talk, by the way. 



#137
Apr1012, 05:53 AM

PF Gold
P: 2,885

In any case, I agree that the "seed top" idea is interesting. The squarks we have are different, as they change barion number. But the diagram at the end of the paper almost fits with the chains from koide, we have also a t>b>c and then a b>c>s, and the point of having the lepton sector hanging separately b>tau c>mu s>e could be similar to the orthogonality.




#138
Apr1612, 06:41 PM

P: 748

I have been reluctant to play the game of conventional MSSM phenomenology  too many possibilities, too much history of "this time, it's just around the corner"  but I have found a psychological startingpoint from which to approach this exercise: think in terms of starting with a "supersplit" spectrum in which all the superpartners are at some ultrahigh scale. You don't start out with the assumption that supersymmetry is the answer to the hierarchy problem or to anything else, and you are spared all the further problemstobesolved that are caused by assuming lowscale supersymmetry. Initially you regard it just as a feature of finalstage unification, extremely remote from experiment...
Then you think "what if one, two, or a few of these particles have small enough masses to be relevant to observable physics after all", and e.g. try to construct a Koide cascade from a HeVolkasWutype theory. And only then do you start thinking about how to get your KoideMSSM from a GUT, from the heterotic string, etc. (The idea of gaugetop unification, or even gaugeHiggstop unification, looks interesting.) If it's worth it, you're even "allowed" to include ideas from conventional superphenomenology, in a specific KoideMSSM model. But in constructing a KoideMSSM, I think it's imperative to start philosophically as if you were just extending the SM, and not the MSSM as conventionally conceived. 



#139
Apr1912, 03:42 AM

P: 748

We may have our first step in a MSSM topseeded mass cascade: a righthanded downtype squark. Dobrescu and Fox (2008) present a model somewhat in the spirit of He, Volkas, and Wu, in which a leptoquark scalar they call "r", and a coloroctet weakdoublet scalar, and some vectorlike fermions, produce a mass cascade in which, starting with a treelevel mass for the top, they obtain bottom and tau at one loop, charm at two loops, and strange at three loops; and muon at three loops and electron at four loops. On pages 910 they note that the downtype squark could play the same role as the "r"  "in supersymmetric models with Rparity violation the squarks may have leptoquark couplings"  though with differences in the details.
There has been a lot of work on radiative generation of SM fermion masses in the MSSM  e.g. hepph/9601262, hepph/9902443, hepph/0107147, arxiv:1108.2424  but it's focused on other sources of mass, e.g. massive gauginos. Nonetheless I think all that work offers a useful context for a detailed development of MSSM topcascade models, e.g. Crivellin (arxiv:1105.2818). There's work on starting just with top, bottom, and tau masses, so if we cut that back to just top, and then put in place a modified DobrescuFox cascade, we might get somewhere. Of course, since we're ultimately trying to explain a cascade of Koide relations, just parameterfitting and showing the phenomenological viability of such a model would not be enough. If this really is how things work, one has to suppose that the Koide relations have an origin outside the MSSM. I suppose it would be convenient if e.g. one introduced extra symmetries to the MSSM just to set nontop yukawas to zero and to get the right structure of couplings for the cascade, and those extra symmetries alone were sufficient to produce Koide relations. But I wouldn't be surprised if we have to go very deep. For example, think of the topological expansion in string theory, in which e.g. a treelevel scattering of n open strings becomes a disk with n insertions on its boundary, and the kloop correction is a disk with k holes. It's conceivable that the Koide relations have their origins in the properties of amplitudes at such a remote level of description. 



#140
Apr1912, 11:36 AM

PF Gold
P: 2,885

About the point of "Assuming that the leptons and quarks other than top are massless at tree level", I still kept a thinking that the M2brane and M5branes should have a role to justify this masslessness. Either that, or something having an 84 irrepr.




#141
Apr2112, 12:05 PM

P: 748

Gaugetop unification occurs in six dimensions. t_R, Q3_L (i.e. the thirdgeneration weak doublet of quarks), and the Higgs all live in the bulk, and the top yukawa coupling is just the unified sixdimensional gauge coupling connecting those fields. (The other SM fermions are all confined to submanifolds.)
Meanwhile, the recently notorious M5brane worldvolume theory is holographically dual to Mtheory (and is thus approximated by d=11 supergravity) on a 7+4 dimensional manifold. The 7 large dimensions are the 5+1 of the M5brane volume plus the usual AdS dimension that is emergent from RG flow. As described on Urs Schreiber's site, this theory also has a description in terms of a 7dimensional ChernSimons theory that can be obtained by truncating the supergravity Cfield for this geometry. It is not beyond imagining that there is a realization of gaugetop unification in terms of M5branes compactified on a particular space, with all the nontop SM fermions being related to the Cfield by a special supersymmetry transformation, as we have discussed before. I don't know if it's at all likely that this is so, but it is a scenario one can imagine and explore. There even seems to be a realization of what I want to call the "(2,3,6) theory" (N=2 susy, 3 colors, 6 flavors) in such a compactification, but I haven't looked into it yet. 



#142
May1712, 03:56 AM

PF Gold
P: 2,885

Not that the blogsphere (ie Dorigo Matt Motl) is burning about nondetection of SuSy, I wonder what are the implications of the wrongturn here. For instance if gluinos decay to quark squark, and squarks are diquarks.




#143
May2512, 09:36 AM

P: 748

Well, let's think about what the "wrong turn" idea is. I've focused mostly on the sBootstrap, which is just a pattern, and in principle that pattern might be realized in a theory completely consistent with conventional thought about SUSY, or it might show up in some strange SUSY theory  maybe highscale SUSY, maybe some peculiar alternative math like Sultan Catto's work.
The idea of the "wrong turn", as I understand it, is alternative historiography which says that string theorists might have figured everything out if they had continued on a path of the very early 1970s. Now what happened is that you had the original constructions of fermionic strings, e.g. by Ramond, you had a few of the basics figured out, and then the standard model revived QFT and almost everyone left strings. Meanwhile Scherk and Schwarz came up with the idea that strings are a theory of everything, which required that the string tension be Planck scale rather than QCD scale. So despite the title of this thread, the "turn" in string theory was not about the scale at which SUSY holds, but about the string scale... I can think of two ways in which bringing the string scale down again might be motivated. One is the largeextradimension models that talk about TeVscale gravity. The other is the revival of "strings for QCD" via AdS/CFT, holographic QCD, and the quest for a string dual of QCD. Also you get the occasional paper talking about TeVscale conformal symmetry, though I don't understand that stuff enough to know whether it's sensible. My attitude to the main line of research since the standard model is that it might be right and it might be wrong. We really could be living in a CalabiYau compactification of the heterotic string. Or we could be living in some different sort of physics that noone thought of yet. Combining a few buzzwords, imagine a twistorial, conformal, noncommutative, asymptotically safe standardmodelplusgravity based on division algebras. :) I think string theory has tapped into math so deep that surely it's relevant to real physics. But the strings we know about might not be the only possible manifestation of that math. So in your question, I think you're asking us to think about the MSSM as if it were 1972, and we had the simple early ideas about dual resonance models, and we had the sBootstrap pattern... what might we come up with. 



#144
Jun1412, 05:43 AM

P: 748

You were asking what highscale supersymmetry might imply for the sBootstrap... One implication of highscale supersymmetry is that SUSY doesn't stabilize the weak scale. But as pointed out here:
But there's still a conceptual problem here: among the motivations for the sBootstrap, beyond the basic pattern of charge pairings, are a few mass coincidences like pion and muon. The dare is to think that these mass scales actually have a cause, e.g. that the muon is a hypercolor mesino whose mass is almost degenerate with the mass of the pion for a reason. The existence of cryptosusy neardegeneracies of mass is at odds with the idea of highscale SUSY; or at least it would imply that SUSY is "broken" in a peculiarly irregular fashion. Then again, this was always so, even before weakscale SUSY began to look problematic. I have a lot more confidence in the meaningfulness of the Koide relations than any of this (like, 99% confidence versus 1% confidence), but the muon/pion and tauon/glueball coincidences are still fascinatingly suggestive, especially if you're looking to obtain the leptons from SQCD mesinos. The heavy charged leptons look like a "collapsed" hadronic sector with only one "meson" (and it's a fermion), and only one baryon. And since the tauon "corresponds" to a threequark object, and the muon to a twoquark object, the electron presumably "corresponds" (in the same dreamlike way) to a single quark. It vaguely reminds me of the difference between ordinary numbers and Grassmann numbers: the ordinary hadrons exist in infinite towers of resonances, but there's just one of each type of charged lepton. Before you dismiss this as sounding too bizarre and arbitrary, consider figure 6 (on page 10) in "Twistor String Theory and QCD", in which the spectra of "ordinary" string theory and twistor string theory are compared. Ironically for the present discussion, Dixon wants to say that the spectrum on the left (with its infinite tower of higher states) doesn't resemble QCD; whereas what I want to say is that the spectrum on the left does look like QCD, and the spectrum on the right looks like the charged leptons, as I have just been describing them! If this was taken seriously, in the context of the sBootstrap, it would suggest that the leptons emerge from a "topological sector" of an SQCDlike theory. 


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