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

[arivero]

As for the relationship between the above folding and the S4 generalisation of Koide, I find that they are two solutions of the eight S4 simultaneus equations that seem relevant:

<br /> \begin{array}{|ll|}<br /> \hline<br /> 3.64098 &amp; 0 \\<br /> 1.69854 &amp; 1.69854 \\<br /> 0.12195 &amp; 0.12195 \\<br /> \hline<br /> \end{array}<br /> \dots<br /> \begin{array}{|ll|}<br /> \hline<br /> b &amp; u \\<br /> d &amp; c \\<br /> s &amp; t \\<br /> \hline<br /> \end{array} <br /> \dots<br /> \begin{array}{|ll|}<br /> \hline<br /> 3.640 &amp; 3.640 \\<br /> 1.698 &amp; 1.698 \\<br /> 0.1219 &amp; 174.1 \\<br /> \hline<br /> \end{array}<br />

The one on the left appears when looking for zero'ed solutions; the one on the right appears in the resolvent of the system when looking for zero-less solutions; so both of them are singled-out very specifically even if, being doubly degenerated, they are hidden under the carpet of a continuous spectrum of solutions.

To be more specific: a S4-Koide system on the above "folded" quark pairings should be a set of eight simultaneous Koide equations, for all the possible combinations: bds, bdt, bcs, bct, uds, udt, ucs, uct. A double degenerated solution of such S4-Koide system lives naturally inside a continuum: the equation K(M1,M2,x)=0, with M1 and M2 being the degenerated masses, has multiple solutions for x, and any two of them can be used to build the non-degenerated pair of the folding.

The solution in the left is one of the possible solutions having at least a zero; up to an scale factor, there are only four of them. I have scaled it to match with the solution in the right.

The solution in the right is one of the solutions obtained by using the method of polynomial resolvents to solve the system of eight equations (actually, we fix a mass and then solve the four equations containing such fixed mass). It is scaled so that its higher mass coincides with the top mass.

For details on the calculation of the solutions, please refer to the thread on Koide.

 

[mitchell porter]

Some recent thoughts:

As with mainstream supersymmetry, I see the sbootstrap's situation as still being one where there is such a multitude of possibilities that it is hard even to systematically enumerate them. The difference is that a mainstream susy model consists of a definite equation and a resulting parameter space that then gets squeezed by experiment, whereas a sbootstrap "possibility" consists of a list of numerical or structural patterns in known physics which are posited to have a cause, and then an "idea for a model" that could cause them. It may be that some part of sbootstrap lore is eventually realized within a genuinely well-defined model that will then make predictions for MSSM objects like gluinos, or it may be that it will be a "minimalist" model that is more like SM than MSSM. (As for the Koide waterfall, that is such a tight structure, it seems that any rigorous model that can reproduce it is going to be sharply predictive - but there may still be several, or even many, such models.)

Today I want to report just another "idea for a model". It's really just a wacky "what if"; I don't know that such a model exists mathematically; but I'd never even look for it if I didn't have the schematic idea. The idea is just that there might be a brane model in which the top yukawa is close to 1 both in the far UV and in the far IR, and that this is due to a stringy "UV/IR connection".

The reason to think about this is as follows. The discussion of whether the Higgs mass might be in a narrow metastable zone, has yielded the perspective that it might be worth considering the top yukawa and the Higgs quartic coupling at the same time. The latter goes to 0 in the UV, the latter goes very close to 1 in the IR.

But Rodejohann and Zhang have observed that with massive neutrinos, the top yukawa can approach 1 at high energies as well (see pages 14 and 15; the minimum is roughly 0.5, reached at about 10^15 GeV). And high energies are where a coupling might naturally take a simple value like 1. So what if there's a brane model where the top yukawa is 1 in the far UV, for some relatively simple reason, and then it is also near 1 in the far IR, because of a UV/IR relation that we don't understand yet? String theory contains UV/IR relations (scroll halfway down for the discussion); none of them appear to be immediately applicable to this scenario; but such relations are far from being fully understood.

At the same time, I think of Christopher Hill's recent papers (1 2, it's basically the same paper twice), in which he first restricts the SM to just the top and the Higgs, and then considers a novel symmetry transformation, which he likens to a degenerate form of susy. At high scales he ends up with the relation that the Higgs quartic equals half of the square of the top yukawa - which is not what I'm looking for. Then again, he also ends up with Higgs mass equals top mass, with the difference to be produced by higher-order corrections. So perhaps his model, already twisted away from ordinary supersymmetry, can be twisted a little further to yield a Rodejohann-Zhang RG flow for the top yukawa, as well as a Shaposhnikov-Wetterich boundary condition for the Higgs quartic.

One might want to see whether this can all be embedded in something like the "minimal quiver standard model" (MQSM), which is not yet a brane model, but it is a sort of field theory that can arise as the low-energy limit of a brane model; and the MQSM is the simplest quiver model containing the SM.

Finally, to round things out, one might seek to realize the sbootstrap's own deviant "version of susy" here too, perhaps by using one of the brane-based "ideas for a model" already discussed in this thread.

 

[mitchell porter]

Krolikowski has some preon musings (relegated to gen-ph) which resemble the sBootstrap. He wants to get the color-triplet SM quarks and color-singlet SM leptons by combining color-triplet preons; but he has to suppose that the preons are a fermion and a scalar boson, in order for the composite to be a fermion, whereas the sBootstrap combines two fermions and then supposes that the phenomenological fermions are superpartners of the resulting composites.

Curiously, in an attempt to explain the up-down mass ratio, he inadvertently provides a new perspective on the Koide-Brannen phase: 2/9 = (1/3)² + (1/3)². He is squaring the electromagnetic charges of the preons for an up quark, on the hypothesis that the mass is a self-energy effect. (The analogous quantity for down is then 5/9, then leading to an up:down mass ratio of 2:5, not too far from the observed 1:2; but he acknowledges that the argument then doesn't work for all the other fermion masses...) I wonder if this completely elementary formula could be motivated in some other context, to explain the Koide-Brannen phase for e,μ,τ?

 

[arivero]

For a different turn... what about the SO(8) in the representations of elementary states of superstring theory?

It seems unvoidable because it comes from taking lorentz group SO(9,1) and decomposing to SO(8)xSO(1,1). So once the worldsheet takes the (1,1) part, the rest must be SO(8). In fact, it seems unrelated to the 7-sphere nor octonions nor other Kaluza Klein thingies.

Could it be posible to have still a "8" representation but under a different group? Of course I am thinking SO(5)xSO(4) or even better, SU(3)xSO(4).

 

[mitchell porter]

There is another installment from Bruno Machet (previously discussed at #149, #172). Machet wants to build the Higgs sector entirely from meson VEVs, with no additional fundamental scalars. John Moffat tried to do the same (#169), and probably there is older literature.

On this thread, #150 forward, there was some discussion of the conventional perspective: without a Higgs, the qqbar condensate will still add mass to W and Z, but they will be MeV-scale, not GeV-scale.

Such works are potentially complementary to the sBootstrap. In the sBootstrap we start with five light quarks, and get all the SM fermions as "superpartners" of the resulting diquarks and mesons, with the uu-type diquarks left over, playing no role in this correspondence, and also no theory of what the Higgs is.

I think I see four possibilities:

1) The Higgs originates outside the sBootstrap combinatorics, e.g. it really is an independent elementary scalar.

2) The uu-type diquarks make up the Higgs field. This is Alejandro's often-expressed dream, but it has the problem that the +4/3 charge has to be mysteriously screened somehow.

3) The Higgs comes from the scalar sector being explored by Machet and Moffat.

4) We could seek inspiration in the recently observed Zc(3900): perhaps the Higgs is a tetraquark! - of the form u u ubar ubar.

 

[mitchell porter]

Some recent papers:

1) A new proposal for quark-lepton unification which resembles Pati-Salam, but with different relations between the mass matrices.

2) The latest from Harald Fritzsch, on making H, W, Z from preons he calls "haplons". It seems unlikely; but what if we thought of the haplons as branes, and the composites as strings ending on them?

3) New d=4 non-susy vacua from F-theory. As Lubos mentions, susy appears if you compactify further, to d=3, so this is a case of hidden supersymmetry; which is why it is relevant to this thread... Also see these old musings by Witten 1 2.

4) Via arivero elsewhere, I have learned of Alejandro Cabo, who wants to get the quark masses from the top quark, via a cascade effect involving condensates; again a theme already explored in this thread. Some of the relevant papers have two "Alejandro Cabo"s as authors, so I am not sure who's in charge, but if you just go to arxiv and look through all the papers with author:cabo, you will find them. Apart from the obvious (titles which refer to quark masses), anything about "modified QCD" would also be part of the program. Especially interesting from the Koide perspective is the appearance of the democratic matrix, e.g. on page 5 here. A. Cabo has also given two talks at pirsa.org on this subject.

 

[MTd2]

4) Via arivero elsewhere, I have learned of Alejandro Cabo, who wants to get the quark masses from the top quark, via a cascade effect involving condensates; again a theme already explored in this thread. Some of the relevant papers have two "Alejandro Cabo"s as authors, so I am not sure who's in charge, but if you just go to arxiv and look through all the papers with author:cabo, you will find them. Apart from the obvious (titles which refer to quark masses), anything about "modified QCD" would also be part of the program. Especially interesting from the Koide perspective is the appearance of the democratic matrix, e.g. on page 5 here. A. Cabo has also given two talks at pirsa.org on this subject.

Talking about Koide relations, do you know Jay Yablon?

http://vixra.org/author/jay_r_yablon

His results are insanely precise for a rather simple method. I'd not say theory though. He calculates stuff differently and get it all too exactly to be good.

 

[mitchell porter]

I have seen his work. The papers which provide formulas for nuclear binding energies in terms of quark masses are a new frontier for physics numerology... What I thought was interesting, is that it is possible at all - e.g. (his starting point) the fact that the deuteron binding energy, and the mass of the up quark, are of the same order of magnitude. In reality, that binding energy ought to be some function of m_u, m_d, m_s, and alpha_strong, that we would currently need lattice QCD techniques to estimate. But I wonder if there is some heuristic argument that apriori it should be within an order of magnitude of the first-generation quark masses? That might be a good question for Physics Stack Exchange or for the HEP forum here... Incidentally, these binding energies also occasionally get mentioned by Arkani-Hamed (and I assume others) as evidence for finetuning in nature - if you look at the effective field theory of nucleons, apparently the parameters are finetuned to several orders of magnitude.

 

[MTd2]

3) New d=4 non-susy vacua from F-theory. Susy appears if you compactify further, to d=3, so this is a case of hidden supersymmetry; which is why it is relevant to this thread... Also see these old musings by Witten [URL="http://arxiv.org/abs/hep-th/9409111"]1 2.

Don't you think it is a nice finding? That is, in the real world, SUSY does not exist, other than a math trick, and string theory is fine with that?

 

[MTd2]

The papers which provide formulas for nuclear binding energies in terms of quark masses are a new frontier for physics numerology...

He justifies his treatment in lengthy papers from standard theory, like QCD. I don't think that is not numerology at all. You have to see if his approximation arguments for QCD are OK. Certainly, it yields results that are OK.

 

[mitchell porter]

Don't you think it is a nice finding? That is, in the real world, SUSY does not exist, other than a math trick, and string theory is fine with that?

String theory has many neglected and disputed corners without supersymmetry. One thing that's interesting here, is that this is F-theory and very mainstream. But in these vacua, SUSY is still there at the highest energies i.e. the compactification scale. It's just different from the usual model-building in string phenomenology, which is to look for something whose low-energy limit has an N=1 supersymmetry that is then broken. Here even that is bypassed, and SUSY is solely a high-scale phenomenon (if I understand correctly).

He justifies his treatment in lengthy papers from standard theory, like QCD. I don't think that is not numerology at all. You have to see if his approximation arguments for QCD are OK. Certainly, it yields results that are OK.

It has only the barest of connections to QCD that I can see. He hardly considers the quantum theory at all, piles guess upon guess (ansatz upon ansatz), freely introduces extra quantities like the Higgs VEV and the CKM matrix into his formulae...

 

[MTd2]

In reality, that binding energy ought to be some function of m_u, m_d, m_s, and alpha_strong, that we would currently need lattice QCD techniques to estimate. But I wonder if there is some heuristic argument that apriori it should be within an order of magnitude of the first-generation quark masses?

He is making a new paper due many requests on further enlightenment. So, if you want to ask question, that's the time!

http://vixra.org/abs/1307.0135

 

[member 11137]

He is making a new paper due many requests on further enlightenment. So, if you want to ask question, that's the time!

http://vixra.org/abs/1307.0135

Since that thread is discussing string theory and SUSY in a kind of fictive and positive competition, I would like to bring a modest contribution in the actual debate and directly ask if the documents pointed here can help the scientific community:
http://www.vixra.org/author/thierry_periat
In a kind of constructive emulation, I would also appreciate any feedback. So far my understanding, a discussion about the vacuum is probably concerning regions with low energies (this is at least the classical and well accepted vision - coming into the debate from the "theory of relativity" viewpoint side). Except if errors (calculations) have been done in one of the proposed documents, the concept of string is not in opposition with the one of vacuum (consequently with the existence of regions with a low energy level). The embarassing consequence is the necessity to accept a dynamical vision for these regions but as far I am well-informed, the 2013 recent analysis of the data coming from the Planck satellite allows a dynamical dark energy...

 

[fzero]

He justifies his treatment in lengthy papers from standard theory, like QCD. I don't think that is not numerology at all. You have to see if his approximation arguments for QCD are OK. Certainly, it yields results that are OK.

Referring to the paper in the Hadronic Journal (which is full of crackpot papers, sorry to say), he bases the whole numerics on postulating that the quark wavefunctions are Gaussian with a width equal to their reduced Compton wavelength. For the up quark, using $m_u\sim 2.3~\mathrm{MeV}$ as Yablon does, the reduced Compton wavelength is $\lambda_u \sim 0.012~\mathrm{fm}$. However, the proton charge radius is $\sim 0.88~\mathrm{fm}$, so the quark ansatze has nothing whatsoever to do with reality.

It's unilluminating to further sift through his classical manipulations or try to point to the large quantum corrections that he waves his hands around (current quark masses are set by the weak scale and unnaturally small Yukawa couplings, whereas the hadronic masses are set by the QCD scale). Instead it suffices to see that the picture of the nucleon that he sets as an input is completely different from what we observe.

I have seen his work. The papers which provide formulas for nuclear binding energies in terms of quark masses are a new frontier for physics numerology... What I thought was interesting, is that it is possible at all - e.g. (his starting point) the fact that the deuteron binding energy, and the mass of the up quark, are of the same order of magnitude. In reality, that binding energy ought to be some function of m_u, m_d, m_s, and alpha_strong, that we would currently need lattice QCD techniques to estimate. But I wonder if there is some heuristic argument that apriori it should be within an order of magnitude of the first-generation quark masses? That might be a good question for Physics Stack Exchange or for the HEP forum here... Incidentally, these binding energies also occasionally get mentioned by Arkani-Hamed (and I assume others) as evidence for finetuning in nature - if you look at the effective field theory of nucleons, apparently the parameters are finetuned to several orders of magnitude.

As I mentioned above, the current masses of the quarks are set by the EW scale (with a huge fine-tuning) and have nothing to do with strong physics. There should be no heuristic argument why properties of the deuteron should be closely related to the current masses.

 

[mitchell porter]

The basic coincidence here is that the QCD scale and the electroweak scale are within an order of magnitude or two of each other. I believe I've seen attempts to explain this anthropically.

One theme of this thread is that the weak interactions and the leptonic sector might be emergent from a strongly coupled supersymmetric theory. There, the benchmark of success might be, to explain the coincidence of scales causally and naturally.

Finally, Koide aficionados have noticed that the basic mass scale in Carl Brannen's reformulation of the Koide formula, is very close to the "constituent" masses of the first-generation quarks. A Brannen-style formulation of Koide's relation, derives particle masses from a common mass scale, and an angle. So it's rather amazing that arivero gets the s,c,b masses by applying Brannen's formula for e,mu,tau, but tripling both the mass scale and the angle. Tripling these parameters might have some rationale involved in working with color triplets (quarks) rather than color singlets (leptons); and then there's the simple fact that three times the constituent quark mass scale, gives you the nucleon mass scale!

So I consider it very rational to at least entertain the possibility that these relations derive from some sort of super-QCD or extended QCD that underlies the standard model... though even if that's true, proving it might have to await future advances in QCD itself, that would make it transparent why quantities such as the nucleon mass and the pion mass have the values they do.

 

[fzero]

The basic coincidence here is that the QCD scale and the electroweak scale are within an order of magnitude or two of each other. I believe I've seen attempts to explain this anthropically.

The QCD scale depends most strongly on the coefficient of the one-loop beta function, which only depends on the number of colors and flavors. Quark masses are a very small effect, but would be the leading way for the EW scale to feed into the QCD scale. I can imagine that it's possible to set anthropic bounds, but I'm not sure that the ratio of the QCD and EW scales is the most important consideration when compared to the fine-structure constant, for example.

One theme of this thread is that the weak interactions and the leptonic sector might be emergent from a strongly coupled supersymmetric theory. There, the benchmark of success might be, to explain the coincidence of scales causally and naturally.

Finally, Koide aficionados have noticed that the basic mass scale in Carl Brannen's reformulation of the Koide formula, is very close to the "constituent" masses of the first-generation quarks. A Brannen-style formulation of Koide's relation, derives particle masses from a common mass scale, and an angle. So it's rather amazing that arivero gets the s,c,b masses by applying Brannen's formula for e,mu,tau, but tripling both the mass scale and the angle. Tripling these parameters might have some rationale involved in working with color triplets (quarks) rather than color singlets (leptons); and then there's the simple fact that three times the constituent quark mass scale, gives you the nucleon mass scale!

This is also numerology. These particles interact, so any dynamical relationship between masses should involve their values at the same energy scale. The Koide-type relations are between pole masses, which have no logical reason to be directly related to one another by a consistent dynamical formula. The difference between pole masses and $\overline{\mathrm{MS}}$ masses might be small for the leptons, but it is not for the up quarks.

I suspect that these are just as coincidental as the fact that the running fine-structure constant is numerically the same as the Higgs mass to within a % or so: $\alpha^{-1}(m_H) \approx m_H/\mathrm{GeV}$.

 

[MTd2]

These particles interact, so any dynamical relationship between masses should involve their values at the same energy scale. The Koide-type relations are between pole masses, which have no logical reason to be directly related to one another by a consistent dynamical formula.

Is nature logical?

 

[member 11137]

... These particles interact, so any dynamical relationship between masses should involve their values at the same energy scale. The Koide-type relations are between pole masses, which have no logical reason to be directly related to one another by a consistent dynamical formula...

But as indicated in arXiv:hep-ph 0505220v1 25 May 2005 (end of page 1 and at the beginning of page 2), these pole masses are co-related in such a way that an angle can be introduced between two vectors: (1, 1, 1) and (m1, m2, m3). This motivates the vision of what one is encouraged to call "directional masses" (masses defining a spatial direction) and at the end this is suggestively asking for the existence of a link between these masses (taken all together) and some underlying geometrical structure... Since the geometrical structure is dynamic within the theory of relativity (Einstein)...

 

[mitchell porter]

the leading way for the EW scale to feed into the QCD scale

I actually had the other direction in mind: e.g. that QCD is embedded in some sort of technicolor where there is a composite Higgs whose properties are correlated with those of the hadronic sector; or, standard model QCD is part of an SQCD whose susy-breaking is transmitted to an independent Higgs sector and determines part of its scalar potential.

As for relations between different energy scales, UV/IR mixing in noncommutative field theory leads me to think that they can exist; though perhaps not in an ordinary field-theoretic framework.

 

[arivero]

The difference between pole masses and $\overline{\mathrm{MS}}$ masses might be small for the leptons, but it is not for the up quarks.

I suspect that these are just as coincidental as the fact that the running fine-structure constant is numerically the same as the Higgs mass to within a % or so: $\alpha^{-1}(m_H) \approx m_H/\mathrm{GeV}$.

I usually do not like when people compares adimensional numerology with dimensional-based numbers, but well, just in this case it is reasonable, and you have a point here, because it is true that fixing a substraction scheme is as arbitrary as fixing a unit. Now, it is good to remember that in adimensional numerology the units are canceled out, and similarly we could find equations which are independent of the substraction scheme, or at least have a very weak dependency.

You have probably not noticed that the final relationship that Porter was mentioning is a relationship between pole masses. Input masses are only the mass of electron and muon, then you get the tau, then the factor three to pass to a Koide equation in quark sector for s,c,b, then Koide equation again to get t from c,b,t, and the final result is 173.264 GeV, to be compared with pdg mass, 173.07 ±0.52 ±0.72 GeV at the time of this post.

Yes it is true that the intermediate results for s, c and b are very near of the $\overline{\mathrm{MS}}$ values given in the tables, but you do not need to buy it in the same package; you can stick to pole mass and still get a fine prediction, 173.26 GeV.

 

[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.

 

[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.

 

[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.

 

[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.

 

[MTd2]

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

 

[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.

 

[MTd2]

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.

Well, you can try to find something here...

http://adsabs.harvard.edu/cgi-bin/n...D..46.5467W&amp;refs=CITATIONS&amp;db_key=PHY

If you find something relevant, tell me!

 

[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).

 

[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.

 

[mitchell porter]

"Superconformal Baryon-Meson Symmetry and Light-Front Holographic QCD"