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

[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.