Monday, October 22, 2018

String theory pros and cons [video - no singing!]

As I mentioned, I used the prize money I got from the recent FQXi essay contest to buy a new video camera. The main reason for doing this was not better music videos (though there’s that), but that my old camcorder doesn’t have a mic port and the audio quality of the built-in mic is miserable to say the least. Turned out, however, that none of my microphones actually worked with the new camera, so you haven’t heard any more of me in the past months than in the prior 10 years.

After too much time in various forums, I finally found a microphone that works with the camera. Miserable failure that I am, I evidently managed to live to the ripe age of 42 without knowing the difference between a TRS and a TRRS plug. But, hey, now I am enlightened! Next problem was that I used the default mic settings of the camera and the result was so incredibly terrible I threw the recordings away entirely and with it went a whole weekend’s work.

Now I believe I’ve found a mic setting that works okay-ish, which is to say that listening to myself does no longer make my toenails roll up. There is still too much echo but that’s an issue which is unfixable for the time being as I have no other place to do the recording. I could have put some filter and compressor on the audio, which I will try next time.

Then of course I noticed once again too late that my white-balance is jumpy. I suspect this isn’t actually something I do, but something I don’t do, probably also some automatic setting that I’d better turn off. Also, I have screwed up my make-up, but you’re probably used to that. All of this is to say it’s more complicated than it seems and really I’d rather stick to writing.

And, erm, “Yadis and Nau” should have been “Nadis and Yau.” Sorry about that. Click on CC in the tool bar to get English captions.


  1. "Und das gibt's jetzt auch in 'ner deutschen Übersetzung"
    (for the germans who didn't get the penultimate sentence)

  2. Abhay Ahsketar just won the Einstein award in October 2018. any chance you could discuss LQG, and specifically Urs objection to LQG on generalized connection?

  3. neo,

    No, I'm not interested enough to look into this, sorry. There's only so much time in my day.

  4. Maybe
    this is a really silly question, but the question
    keeps me awake all nights since years: :=)
    are there hooks where those strings are fastened to?
    Or do they have some stiffness? In this case the name
    is inappropriate of course. And: can a one-dimensional
    object have "stiffness?

  5. ok,

    let me rephrase, can you create another similar video for LQG, and your conclusions on whether it is interesting and whether it is promising, like you did for strings, with cons then pros. and another video on asymptotic safety.

  6. Sabine,
    I didn't notice any problems with your white balance, make-up, microphone etc.
    I enjoyed your video.
    It turns out that you don't look like your profile picture at all.

  7. The history bit about string theory starting out as an attempt to explain the strong nuclear force sounded familiar. Then I realized I heard a similar explanation in a very recent episode of PBS Spacetime:

  8. the thing is this. i think there's a difference between 'anything could happen because we don't have a paradigm' and'anything could happen because we have a paradigm and that is a prediction of it'.

  9. Dear Sabine,

    I am following your blog with great interest from the sidelines (me working in condensed matter physics)!
    I found it amusing that today an advertisement appeared all over on your blog pointing to this link:
    www dot quantumspaceelements dot com

    which is obviously somebody trying to sell a fake theory.

  10. Do you do the captions yourself or is that automated?

  11. Thanks for the video, clearly explaining pros and cons of String Theory.
    However, I missed the mentioning of the Braneworld development of String Theory, which at least avoids any dark energy inflation (Steinhardt et al.).

    As an aside question: What do you think about Vafa's recent "Swampland" conjecture (apparently conflicting with the Higgs potential) versus Susskind's String Landscape and the Multiverse?
    Greetings from Switzerland
    Rene Kail

  12. MiaZZa,

    Sorry about this. The way that Google Ads works is that you pick a category and then the ads roughly fall into this area, but of course there's the occasional crank with money who thinks that an advert will help him sell his theory. I could try to veto this particular ad, but it's rather pointless as these people are legion.

  13. Andrew,

    I typed the transcript, had the timing set automatically, and then fixed it in some places where it was particularly weird (eg, single words).

    Google does offer automatic transcription, and I was trying to use that but it didn't work. For whatever reason the automatic transcript that appeared was in German. Or rather, it was the attempt to assign German words to what was actually English. It was complete gibberish.

    I then deleted this but couldn't get YouTube to redo the automatic transcript in English (the option was missing from the menu). So I had to transcribe it myself. There is probably a better way to do it but at this point I wasn't in the mood to spend an hour looking for a smart software to do a transcript that took me 15 minutes.

    The automatic transcript btw doesn't work at all for music videos, as you can probably guess. Usually not even the time-setting works in this case.

  14. rhkail,

    I don't know what you mean by dark energy inflation, I think you are confusing two different things. There are various ideas for string cosmology but I count those as phenomenological models, not string theory proper. As to the swampland, I mention this as "the newest problem that people are discussing" starting at 5:17. Best,


  15. I think Leonard Susskind explains some of the history of string theory in the first lecture (at the very start) of his Strings Theory and M-Theory online course:

  16. It looks like your sudden eye dilations (e.g. at 0:02 and 0:25) were inspired by Bert‘s at 0:41 in the video below.

    If you think that string theory is weird, it‘s because you don‘t remember the 1960s. (Of course, some claim that no-one who experienced the 1960s actually remembers them.)

    I‘m not sure how many readers have the background to appreciate how off-the-wall this video actually is.

  17. This comment has been removed by the author.

  18. Baryogenesis requires chiral anisotropic vacuum. What part of physical theory allows that? One cannot imagine why physical theory does not predict observation. Perhaps accepting what is observed is cheating.

  19. @Pmer

    The science paradigm is theories must predict specific observations. Theories that predict anything observable and unobservable are metaphysics.

    “The mind of God is music resonating in 11-dimensional hyperspace.” (actual quote from famous string theorist) The Indian mystic Maharishi Yogi taught the unified field of string theory, transcendental meditation and levitation. This is the theology-mysticism-string-theory paradigm shift.

  20. Ari,

    I have a patreon account but don't use it. I looked at this service some while ago but they expect some regular production schedule - this doesn't work for me. You can support me using the donate button in the top right corner. (Or buy my book.)

  21. Ari,

    I have a patreon account but don't use it. I looked at this service some while ago but they expect some regular production schedule - this doesn't work for me. You can support me using the donate button in the top right corner. (Or buy my book.)

  22. This kind of video feels very non-constructive. Let's say for sake of argument that string theory is a failure as a TOE. What should theorists interested in quantum gravity research instead? Is any of the other proposed theories more promising?

  23. hopffiber,

    Read my book, I explain what they should do instead.

  24. @ George, Open strings are attached to D-branes with Dirichlet boundary conditions, which means fixed in space, or to N-brane with Newman conditions with fixed momentum. The anchor is then a sort of charge at the endpoint of the string called a Chan-Paton factor. One can think of an open string, a type I string theory, as similar to a meson with two quarks tied together by gluon flux lines that are self-bound into a narrow tube or string.

    I will watch the video here in the evening when I have a bit more time.

  25. George, I was also going to reply to your string question but forgot. I will answer from a mechanical-engineering point of view (not as technical as LC's).

    A string does not have bending stiffness, but it does have tension stiffness (otherwise guitar strings and bow strings would not work). With just mass and tension-stiffness a string can vibrate, although without the ends fixed the first natural frequencies are very low compared to with ends fixed and under tension. A circular string (no free ends) also can vibrate. As I understand it, string-theory (in atomic physics) began when someone (I forget who but you could look it up) noticed that the theoretical string frequencies matched some parameters of atomic particles.

    Think of a spring with masses on each end, or several small springs connected by masses. That is actually how a free string could be modeled to calculate its frequencies (in a "lumped-mass model"). Assuming your question was based on the assumption that a free string cannot vibrate, that should perhaps clarify it for you. (I hope.)

    In a more perfect world, everyone would study a little mechanical engineering, as well as physics, computer-programming, a musical instrument, etc.

  26. Your criticisms are fairly on point. String theory describes a world with a negative constant curvature or equivalently cosmological constant and with gauge fields associated with gravitation, equations 12.3.27-28 in volume 2 of Polchinski's book String Theory illustrates how additional fields enters in with gravitational connections. It is in a lot of ways a world apart from the one we directly experience.

    If you though go back and look at string theory its original setting is in 26 dimensions and the string world sheet is really an advanced treatment of the complex plane with Virasoro algebra for analytic functions. The 26 dimensions come from an anomaly cancellation that gives unique commutators of operators X_n = z^n∂/∂θ, z = re^{iθ}, and it is easy to see that [X_m, X_n] = i(m - n)X_{m+n}, which is the Witt algebra. To remove a degeneracy of commutators a center exists that defines the anomaly cancellation and requires the associated spacetime on a target map have 26 dimensions. To cure the problem of that many dimensions supersymmetry reduces this so that 26 dim = 10 dim spacetime plus rank 16 group.

    The 10 dimensions and compactification of 6 of those dimensions is the idea of Kaluza-Klein theory. This goes back to the early 1920s when the two fellows derived this for electromagnetism with gravity. The cyclicity condition that derivatives of spacetime with respect to the additional dimension restricts this additional dimension to a circle. With 6 dimensions things are a lot more complex with Calabi-Yau spaces. This is of course where string theory gets very complex.

    My take on string theory, knowing a fair amount about it, is there are likely some stringy aspects to the quantization of gravity and unification. What I do not uphold in quite the unquestioning way I have seen is the idea string theory is all.

  27. @Lawrence
    Those are all nice strings. Reminds me of a remark by Sheldon Glashow, Medieval theologians debated how many angels can dance on the head of a pin. String theorists replaced the angels with Calabi-Yau manifolds.

  28. The Calabi-Yau manifold appears in basic electromagnetism in an indirect way. The gauge field occurs because there is a quantum phase e^{iθ} where the phase angle depends on position. To remove this phase dependency the momentum operator is made covariant P = p + ieA, where A is the vector potential of electromagnetism. The phase e^{iθ} is a circle on the complex plane. This circle has a target map onto a small circle in an additional fifth dimension.

    Gauge fields are modeled as an internal space in a Cartesian product with spacetime at every point. This is standard stuff. I heard a story that either Kaluza or Klein who after finding 5 dimensional general relativity with the fifth dimension curled up gave Maxwell's equations started to sing out loud the Ode to Joy of Beethoven. Einstein was fairly taken with this idea.

    The simplest Calabi-Yau manifold is a torus, which is just the generalization of the circle. This configuration does not work. Other more complicated topologies have been explored, many with projective geometric structure. The number of possible compactifications is enormous as this is equal to the estimated number of topologies. This is where the magic number 10^{500} comes from. Now talk about wrapping D-branes on these and working string theory! At this point one has to wonder if things are begging for something else.

  29. @Lawrence Crowell "the magic number 10^{500)"
    … 10^723 string theory standard models

    These same people decry one day in a microwave spectrometer to the contrary: too high a risk of failure to be run because baryogenesis has only empirical validity. There is no fire, there is no pony, the Emperor is naked. My graphs have a zero in each abscissa and ordinate.

  30. @hpoffiber: You ask "What should theorists interested in quantum gravity research instead?"

    If they knew what they should research, they would be researching it.

    There are hundreds of very smart people thinking about string theory, and they aren't getting anywhere. If they could instead switch to looking for alternatives to string theory (something they probably can't do right now because of the way that we fund physicists), they might come up with a promising direction.

    Certainly, looking for a new path is better than blindly trying to follow the dead ends that all the string theorists have been exploring for the last thirty years without getting anywhere. And if you don't understand why they're dead ends, read Sabine's book.

  31. Just wanted to add that, to my (very limited) knowledge there are two other significant "predictions" from string theory. One is measuring the entropy of a black hole by counting microstates. That's not an experimental test, but is a kind of mathematical consistency cross-check. The other is a predicted minimum ratio of viscosity to entropy density. See, for example, The perfect liquid -- now even more perfect. Heavy-ion experiments RHIC and ALICE have measured the entropy of quark-gluon plasmas, and get results a little above (inside) the limit predicted. I haven't heard anything new about this test in the past decade, but it actually seems like a valid way in which string theory could have been invalidated, but was not. I don't know if Lattice calculations predict the same results or not. As far as I know, these fluid properties are intractable in LGT so probably the jury's out. The article cited here lower limits for non-isotropic plasmas, but I think the plasmas created in the lab thermalize very quickly and may thus be isotropic.

    It's hard to call these real successes of string theory, but I do think they are noteworthy. As usual, I'm probably wrong about this. I post here in order to find out why I'm wrong, not that I'm wrong.

  32. Some how you managed to identify all the things about string theory development that have never made sense to me. As always THANK YOU for sharing your insights.

  33. According to the Hitchhiker's Guide to the Galaxy, the answer to life, the universe and everything is… 42^500 string theories. Then the hyperintelligent quantum supercomputer created Earth to find the question.

    1. Actually the answer to life and everything was 16. Deep Thought just misprinted 4^2 ;)

  34. Bee, and anyone else

    if LQG in 4D is "wrong", is the idea of a canonical quanitzation of some form of gravity that reproduces GR in 4D a promising approach to QG, even if one specific way to do it, LQG is incorrect, the general idea of doing this?

  35. Topher,

    As I explain in the video, the black holes that string theorists do their calculations for live in anti-de-Sitter space. I don't know how this is relevant for anything. It's great if they manage to produce a construct that at least is not internally inconsistent, but so what? Also, I strongly doubt that this is even consistent because of the firewall issue.

    For what the entropy (density) bound is concerned, this result has been pulled into question by condensed matter physicists (see eg 1504.07131) and experimental test is pending. Or maybe the bound isn't actually a bound, see eg 1801.08627. Indeed, string theorists have made somewhat of a habit of conjecturing bounds which hold until they don't, basically. In other words, they're conjecturing things and counting on experimental test being in the remote future. Best,


  36. Bee,

    i thought the issue with black hole entropy in strings was it was only calculated for extremel and near-extremel black holes, but not uncharged black holes.

  37. neo,

    Yes, that too, but I believe this to be a solvable problem. That these calculations only work in AdS, otoh, I think is an unsolvable problem.

  38. Neo,

    The stringy content is often in BPS charges. This pertains to extremal black hole, which in this setting is a sort of ensemble of elementary quantum units of black hole. The black hole is placed in an AdS, which is the only possible "bottle" that can hold a black hole. Remember Gauss' law and that any massive shell around a central mass is not gravitationally coupled to that mass. I also wrote how the near horizon configuration of a black hole for a static observer is AdS_2xS^2. There is then some AdS-black hole duality principle, though the stringy quantum black hole only works in an AdS background.

    The AdS is not the world we observe. The connection of the de Sitter (dS) spacetime is as yet unknown. I usually like Susskind's lectures, but one I watched on the dS/CFT duality he works on was painful to listen to. Is this unsolvable? I am not willing to say that, for there are lots of interesting ways of transforming spacetimes into other spacetimes, particularly if you are versed in the Petrov methods.

    String theory is just grist for the mill. How it fits into some emergent big picture is not clear. It may be in the gemish, but I rather suspect it may be a bit on the margins relative to some new principle.

    Never say never. I have some deep suspicions about ideas of sending people to Mars, colonizing space and the like, but I do not think it is impossible or that it will never happen.

  39. I meant to send this link with my last transmission. It illustrates the AdS connection with black holes.

  40. Dr. Hossenfelder,

    Do you have any information on the percentage of funding that is directed to string theory?

    Or how about a chart showing arXiv papers focused on string theory by year?



  41. bee, lawrence,

    thanks. but if it is potentially solvable, why in all these years (decades? - since the extremel result was offered in mid 90s iirc) hasn't it been provided in non-extremel case (in AdS)?

    Bee, without going into great detail, can you explain in a sentence why you think the issue with black hole entropy in DeSitter can't be solved in string theory?

    and does the problem of (nonextremel) black holes entropy in Desitter space also apply to LQG, spin form asymptomatic safety calculations ?

    is LQG/spinfoam the only QG candidate theory that can provide a black hole entropy calculation for non-extremel black holes in Desitter space?

  42. neo,

    I think there have been some papers about near-extremal black holes & it seems to me that those methods can be extended to the general case. Frankly I haven't followed this because I consider it a waste of time anyway and I have better things to do.

    As to why I don't think the AdS case will help with the dS case, I have explained this elsewhere, but here we go again: There is no reason to think the limit \Lambda->0 is continuous. Indeed there are many reasons to think it is not. The very fact that Hawking's calculation in asymptotically flat space doesn't show significant departures from pairwise across-horizon entanglement until the very late phase (where nobody knows what happens) tells you that the BH-entropy doesn't count microstates, which flat out contradicts the AdS results. Or, let me put this differently, the limit of a sequence of spaces with boundary isn't a space without boundary.

    You should talk to some string theorists about this, you can have some fun with that.

  43. bee thanks.


    " Frankly I haven't followed this because I consider it a waste of time anyway and I have better things to do. "

    i thought your research interests were in QG and included black hole physics, entropy, though i know your most recent papers were in covariant gravity and MOND

  44. Your video is well done except that some of the books you showed never got completely in frame. But that is no matter; Mr. Google makes it easy to find them even with only partial info.

    Thanks for your work.

    sean s.

  45. Bee: I wish wormholes where possible so I could extend a hand over to your side of the world to shake your hand. Your intuition or thinking that Λ → 0 is not continuous may be entirely correct. This is a feature of BTZ black holes that have a duality with AdS_3. I will try to make this gentle and this is in part due to Witten in his paper arXiv:0706.3359v1 Three Dimensional Gravity Revisited.

    With AdS_3 = SO(2,2)/SO(2,1) the isometry group SO(2,2) = SL(2,R)\times SL(2,R) defines the invariant group state. Each SL(2,R) gives the left and right movers. The CFT gauge-like physics for the left and right fields is governed by each SO(2, 1) with the coupling constant (c_L, c_R) = (24k_L, 24k_R) with ground states k_L and k_R. The difference in these ground states k_L - k_R is integral in units of Planck energy. Conformal theory in 1 + 1 dimensions has ground state energy -c/24, which with the embedding of AdS_2 → H^2 ⊂ AdS_3 reflects a single valued vacuum. In general with left/right fields we now have a discrete spectrum. A consequence of this is the J-invariant Klein function that builds the partition function for a black hole converges to the Bekenstein result as the number of quantum states or qubits N → ∞.

    However, the astute reader might ask, how is this condition discrete for Λ → 0 which corresponds to a cosmological horizon distance of d = sqrt{3/Λ} → ∞ and is then N → ∞ on a Bousso bound? Thus enters in a gadget from string theory called T-duality. This really is just the linear fractional transformation of SL(2,Z), x → (ax+b)/(cx+d) and is a quotient factor that defines the moduli space. So while the horizon scale may become large the momentum dual becomes small and this discreteness emerges again. This means indeed there is a discrete nature of the

    Subir Sachdev has pioneered the use of string theory ideas in solid state physics. As I work on solid state physics I tend in some ways to go the other way. The de Sitter and anti-de Sitter spaces (dS/AdS) meet at I^+ and in their embedding space form the two hyperboloids, the dS the single one and the AdS in two pairs. In the momentum space, remember the argument in the last paragraph, these are bounded by a Dirac cone with a mass-gap. This is how edge states are formed for Mott insulators with topologically protected symmetries. So quantum mechanically or with quantum gravity there can't be a continuous transformation Λ > 0 → 0 → Λ < 0 connecting the dS and AdS.

  46. neo, should I ever write a paper about BPS black holes in AdS, please hit me over the head and throw me in the gutter.

  47. Lawrence,

    That's an interesting point and much sharper than my rather vague elaboration. There seems to be a sentence missing in your comment, however, maybe you can fill in the blank.

    What you say is much sharper because from what I said you could argue (and I have spoken to people who have argued this) that you just don't care: You can simply define the flat-space case as the limit \Lambda \to 0 and disregard the question whether that's continuous. I don't see how this would help with the transition you discuss though.

  48. Oh, yeah, that's another one of those "arguments" I am tired of hearing: Money is wasted elsewhere too, so who cares? Well, I care. Wasting money on 15,000 people to produce math-fiction means 15,000 other people whose research could benefit mankind are not getting paid.

    Since someone above asked for numbers, a quick estimate is $100,000 per person per year. It's somewhat less for postdocs, somewhat more for tenured faculty. On the average it should be okay. Let's say you have 2,000 string theories who you pay for 30 years, that's 2,000*30*100,000 = $6 billion. Or, for the foundations of physics in total, $45 billion.

  49. (That, of course, does not include expenses for experiments.)

  50. Bee,

    The point is there is a mass gap that prevents the occurrence of Minkowski spacetime. The T-duality of qubits, or to avoid stringy language the hyperbolic discrete transformations of conjugate variables or quantum observables, means the departure from Bekenstein's bound for small N and convergence as N → ∞ to that bound. This is a dual interpretation for momentum p ~ 1/Nℓ_p with departures as p → 0, and in stringy context is what interchanges type IIA and type IIB strings.

    A part of this involves demolishing the generalized uncertainty principle of string theory

    ΔxΔp ~ ħ(1 + α'Δp^2)

    which I have always thought was ugly. A gauge theoretic type of result I think can cancel this out sod we get ΔxΔp ~ ħ and the beauty of QM restored. This is an argument based on beauty that might just reflect an aesthetic bias. Curiously something similar goes on the LQG theories with double and scale relativity. In fact the thought has occurred to me the two in some way cancel each other's

    This would then mean the most basic spacetime of special relativity is not stable or does not exist. This gap though is a boon for ideas of chronology protection and cosmic censorship. Unless we have some blinders on that prevent us from seeing we are in the Twilight Zone, we are then prevented from the craziness of time loops and we do not live in an AdS spacetime.

  51. I have to give a hand to Bee's counter argument to the money argument. This is rather typical these days, and is employed to knock not just theoretical physics but everything from art to astronomy. So goes this rather stout type of argument, where it implies we should be hedge fund managers, or some such. Really??? What good in the end do the investor class generate other than grab more money for themselves? Then for those not in the elite classes should then shut up and be content in this new age of working for the app as say Uber drivers.

    Gordon Lightfoot has a line in his song Too many clues in this room, which has some relevancy for this blog in a way, "Praise the Lord there's a train leaving soon." As time goes on I can seen the power of this --- get me outta here!

  52. Sabine

    i'll remember to do that lol.

    since your background is QG, of all the QG candidate theories out there, that is professionally researched,

    is LQG the only candidate QG that is compatible with deSitter spacetime and reproduces Black hole entropy in DeSitter spacetime, unlike string theory?

    if so, shouldn't more research attention be given to LQG?

    in effect, the observation of a positive cc is an "experiment" and string theory fails this experimental test, LQG passes it. (not sure about other candidate QG theories)

  53. neo,

    Asymptotically safe gravity is perfectly compatible with a positive cosmological constant, and I am not aware that it is a problem for causal dynamical triangulations. Causal sets famously predict the cosmological constant (as in: actually predict, not post-dict), and some approaches to emergent gravity come with a cosmological constant by exploiting that it appears in the MOND-limit. (In a sense you get the cosmological constant from dark matter.)

  54. yes, but the second constraint,

    do they also correctly reproduce Hawking entropy and radiation for black holes?

    in addition to positive CC

    LQG apparently does both.

  55. neo,

    No one knows what the "correct" entropy of a black hole is because no one has measured it. And any theory that reproduces the semi-classical limit must reproduce Hawking's result for the radiation.

  56. Sorry, string theory skeptics, but string theory will not be going away. It's too connected to gauge theory and quantum gravity, it's too flexible to be abandoned even if the susy-GUT synthesis isn't working out, and it's too close to reality and too potentially predictive to just ignore.

  57. Unknown,

    First, I say this constantly: If you really want to post as "Unknown" could you please at least enumerate yourself? How is anyone supposed to know now whether you are the same Unknown as the earlier one?

    Second, I actually agree with this. I don't a priori have problem with people who write stories - of the math-kind or of the verbal kind - because we may have a human need for stories. It's all fine with me if someone wants to spend their life thinking about and writing about the multiverse, and I can understand that people like to read about it. I just have a problem if someone tries to sell those stories as science.

  58. @Georg,
    good thinking.. except the hooks. LQG proved background independence is required.
    A string with stiffness is a Band... and the topic of my DPF '15 paper. Bands have three natural quantum-distinct ground states, which the band oscillates between. That yields an ideal representation geometry for neutrinos. They can also model QC/ED state algebras.

  59. Sabine,
    The story you tell of the pitfalls and theorists determined efforts to diagnose its fundamental issues was quite interesting. It kind of reminded me of bug-checking a huge messy program, in which the root cause has not yet been found... lots of work-arounds and fixes...making everything all the messier.

    IMHO, the string as representation geometry story goes awry very early - in Green-Schwartz-Witten's book about pages 25-28, in fact. There they press on with an implicit assumption that the closed string is cylindrically symmetric with perturbations. (As we shall see later, the curvature /perturbations model energy..)

    Well, would it not make MUCH more sense to encode a solution to quantum algebra problems at root-geometric level? That is, simply map chromodynamic local gauge fields to partitions of the string. This fundamentally gives a spinning 'string'/(band) a chromo-quantum! No searching for QCD algebra - just build it in!

    .. and the rest of a particle's physical properties can also be represented 1-1 and onto with Std Model. I've published and presented that in 1992 and many times since. The arXiv paper unfortunately is from a time when publishing color figures was prohibitively expensive... they all appear in later online publications, tho. .. I'd give the links to DPF proceedings papers/slides but the bee rules seem to discourage that... Wayne


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