Experimental Predictions From F-Theory

I’ve been known to claim that string theory makes no experimental predictions, so this evening thought I better take a look at a preprint that just appeared entitled GUTs and Exceptional Branes in F-theory – II: Experimental Predictions. The abstract claims that to have found “a surprisingly predictive framework”.

This paper is 200 pages long, and a companion to part I, which was 121 pages. For part I, there’s a posting by Jacques Distler that explains a bit of the very complicated algebraic geometry going on. Making one’s way carefully through the entire 200 pages of the new paper looks like a very time-consuming project, so I thought I better start by identifying what the experimental predictions are. These days, one expects experimental predictions to say something about LHC physics, but I don’t see anything about that in the paper. Perhaps this is because, except for some comments in section 16, it appears that the authors are studying a model with exact supersymmetry.

Looking at the introduction and conclusion sections of the paper, the only predictions I can see are for neutrino masses, and there are two of them. Either .5 x10-2 +/-.5 eV or 2 x 10-1 +/- 1.5 eV is given for the neutrino mass, with the error bars just those due to an unknown value of one of the geometrical parameters involved. There’s no mention of which neutrino is being discussed, and as far as I can tell this is just an order of magnitude estimate of the neutrino mass scale, one which the author’s describe as “somewhat naive”, noting that “factors of 2 and π are typically beyond the level of precision which we can reliably estimate”. It’s unclear to me whether or not other mechanisms giving quite different neutrino masses would also fit into the author’s model.

Maybe I’m missing something and an expert can help me out, but I’m not seeing anything here of the sort one would normally describe as an experimental prediction. There’s certainly nothing falsifiable at all about the model, since one knows from limits on neutrino masses and measurements of oscillations that the neutrino mass scale has to very roughly be in this kind of range. Furthermore, again maybe I’m missing something, but I don’t see any way in which more detailed calculation in this framework can make it any more predictive.

Update: Lubos has a detailed posting about this, and from reading it, it doesn’t appear that the paper has experimental predictions that I missed. I do wonder what a “musculus maximus” is…

Update: For more about this, see presentations at PASCOS 08 here and here. The first describes this as “a modest step” in the direction of predictions, the second doesn’t mention predictions at all.

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29 Responses to Experimental Predictions From F-Theory

  1. GR says:

    I’m a physics undergraduate who’s interested in this sort of thingl… if I wanted to decide things for myself, where could I start?

    Obviously it takes many years of hard work to develop the math skills (not to mention vocabulary), but is there a reasonable introduction so I can start to understand the crazy things people talk about these days in HEP theory?

  2. GR says:

    Also, and hopefully not as off-topic as the above, the old joke comes to mind:

    Engineers are happy to get an answer to a few decimal points.
    Physicists are happy to get an answer to an order of magnitude.
    Astrophysicists are happy to get an answer to an order of magnitude in the exponent…

    Can we substitute string theorists into the punchline now?

  3. Peter Woit says:


    Well, I wrote a whole book aimed at you, and it contains lots of recommendations for further reading.

    I don’t recommend trying to understand what is going on in this kind of paper. It involves a huge amount of technical background, in both math and physics, and by the time you would be able to absorb it, LHC results almost certainly will have made it irrelevant. Study quantum field theory. It’s a huge subject, and will be there in the future no matter what.

  4. Luboš Motl says:

    Dear GR, a standard textbook that introduces students to modern geometry, algebraic geometry, and similar subjects that are needed in the F-theory model building is one by Nakahara.

    Click my name, go to my blog, and a link to the amazon.com page of the book is included in the article.

    Unless you want to become a complete idiot, I recommend you to pay no attention to Peter Woit and his blog. He is just an aggressive crackpot who tries to revenge to physics for the fact that he is unable to do it himself.

  5. Gil Kalai says:

    Hi Peter, this post is related to quite a basic question in the evaluation of scientific theories, (and also related to basic issues in statistics.) According to all major philosophy of science theories, e.g., both the Popperian falsification approach and the Bayesian verification point of view, scientific theories should be judged based on their ability to predict and not based on their ability to explain known observations. Still in reality, most scientific theories were created in order to explain known observations. Predictions as well as empirical proofs based on fresh observations came much later. Trying to connect a theory to what “one already knows” while falling short of an “experimental prediction” can be of interest.

  6. Sara says:

    “a complete idiot”? Luckily you are an intelligent person and a very very well-brought-up man.

  7. Peter Woit says:


    Sure. I’m just trying to figure out why the authors put “experimental predictions” in the title of this paper.

  8. M says:

    do they predict that neutrino masses are of Majorana or of Dirac type?

  9. Peter Woit says:


    As far as I can tell they predict both, with one of their mass ranges a Dirac prediction the other Majorana.

  10. Mark says:

    A somewhat related thought: In the mathematics literature if you want to find out more about what the main results of a paper are you can try its mathscinet review.

    Is there any kind of broad (online) database for what various physics papers predict from the outcome of proposed, as yet unconducted, experiments?

    (Perhaps I should have posted this in the comments for the INSPIRE post?)

  11. Garrett says:

    Hi Peter,
    I’ve been sitting in on some of the PASCOS 08 talks here at the Perimeter Institute this week. Cumrun Vafa gave a talk yesterday, which Perimeter already has up here:


  12. Peter Woit says:

    Thanks Garrett,

    I see that in slides introducing his talk, Vafa agrees that string theory does not make “a verifiable quantitative prediction for the real world”, and that this work is only “a modest step in that direction.”

  13. Garbage says:

    I haven’t read the paper, but for one thing…it is a hep-th

    Regarding SUSY, they say in the abstract:

    “Communicating supersymmetry breaking to the MSSM can be elegantly realized through gauge mediation. In one scenario, the same repulsion mechanism also leads to messenger masses which are naturally much lighter than the GUT scale.”

    So they do address SUSY breaking…

  14. Peter Woit says:


    If you do take a look at the paper, you’ll see that my remark that only in one section (16) do they address supersymmetry breaking, and then basically just to say that they could break supersymmetry if they wanted to.

    So, I guess the idea is that on hep-th, the term “experimental prediction” means something different than elsewhere?

  15. Sanjay says:

    Dear GR,

    In addition to Nakahara’s book, I would also recommend Tu’s Introduction to Manifolds followed by Bott and Tu’s Differential Forms in Algebraic Topology. All three are excellent and Nakahara gives a very physical picture of the mathematics. As for QFT, there is a whole range of books, but for a solid introduction look at both Zee’s Quantum Field Theory in a nutshell and Srednicki’s new QFT book. Also, Tom Banks’ new QFT book should be coming out soon.


    Good luck with your studies!

  16. Alex Mikunov says:

    Lubos has to stop creating paradoxes (e.g. “…I recommend you to pay no attention to Peter Woit and his blog…” while posting on the P.W.’s blog 🙂 and get back to M-theory (or whatever currently its name is). Otherwise he’s really boring

  17. Peter Orland says:

    Dear GR,

    I fear you are being led down the garden path (or whatever the hell the metaphor is) by my esteemed friends and colleagues.

    If you really want to learn about theoretical particle physics (or theoretical condensed matter physics), learn quantum field theory. This means functional methods, scattering amplitudes, renormalization
    and critical phenomena.

    You will have to read and understand a good graduate text on quantum mechanics first. General relativity (your initials) is also useful and much easier to learn than QFT. Algebraic geometry, algebraic topology, differential topology, …. are nice, and some advanced concepts in QFT, require knowing these subjects. But they are just pleasant diversions until you know basic QFT.

  18. somebody says:

    While we are all giving advice: I would second Peter O.’s recommendation. Don’t focus on the math. The math will come, when you need it. Same is true about GR. Learn QFT. By that I mean know everything inside Srednicki’s book. Which in my opinion is the best book out there. Don’t get distracted by too many books if you can help it, but this is not always easy. If you can work through Srednicki cover to cover, you are already pretty powerful. By the time you finish that, hopefully you will know what to do next yourself.

  19. Sam says:

    Peter, you will be pleased to learn that musculus maximus is defined at:


    I’m sure you’re not shocked… 😉

  20. Aki says:

    “I do wonder what a “musculus maximus ” is…”

    Supersymmetry in human body, i guess 😉

  21. Indrajeet says:

    You have not written anything about the recent work of Sunil Mukhi and co. from TIFR which has “led to a mini-revolution in the theory of membranes”.

  22. Brini says:


    this is not too much of a surprise. Woit, who hastened to write after attending a talk by Berkovits, that

    “it would be pretty damn funny if it turns out that multi-loop superstring amplitudes aren’t finite”

    and who started an infinite blogwar against Distler on string perturbation theory a couple of years ago, has completely overlooked the recent papers by Grushevsky, Cacciatori et al on genus 4 amplitudes. He probably hasn’t found them “funny” enough 🙂

    Personally, I just find it more and more difficult to consider fair such a blind, biased and emotional criticism of string theory, let alone to see its scientific foundations – if any.

  23. Thomas Larsson says:

    You might want to have alook at this and that posts by Jacques Distler. Punchline: “That was fun while it lasted”.

    The Nambu bracket is a kind of Jacobiator. I don’t associate with Jacobiators.

  24. The Nambu bracket is a kind of Jacobiator.

    I tried to make sense of a statement along these lines but was not really happy with what I got. Do you know more? I’d be interested.

  25. Peter Woit says:

    Indrajeet and Brini,

    I keep a list on my desk of topics I’d like to write about, but haven’t gotten around to for one reason or another.

    One item on the list is the activity surrounding the so-called Bagger-Lampert model, a new 3d superconformal model. I haven’t written about this because I don’t know much about it. I haven’t spent time learning more partly because I recently asked an extremely distinguished expert on the topic about what one could do with it, and he told me he wasn’t aware of any really significant implications. Maybe I misunderstood him and am misrepresenting his views, but this seemed like a good time to wait a bit and see what emerges from all the current activity. Thomas’s link to the latest Distler posting shows why following one piece of this, the Mukhi et. al. work, might not have been worth the time. For now, I think I’ll stick to my decision to wait and see what comes out of this, if there is something really significant, many review articles will be appearing later this year. I’d of course be happy to hear from anyone who can explain more about the significance of Bagger-Lampert.

    The work of Grushevsky et. al on multi-loop amplitudes is also on the list, awaiting my finding time to consult with experts and better understand its significance. My understanding right now is that a conjectured form for 3 and 4 loop amplitudes has been found that satisfies the various stringent consistency conditions one expects, but that this is not an actual derivation from the definition, but I may have this wrong.

    Previous arguments on this blog were about the question of whether a proof of finiteness of super-string theory amplitudes exists. I’ve always said that the situation is that it is likely that these amplitudes are finite to all loops, but that this remains to be shown. People are still working on the Berkovits pure-spinor formalism, but as far as I’m aware, it still does not give a proof at higher loops. The work of Grushevsky et. al. certainly pushes the subject forward and removes some possible places a problem could turn up, but as far as I know, it also does not provide a finiteness proof.

  26. Thomas Larsson says:

    According to the appendix of arXiv:0712.3738v2, Andreas Gustafsson has shown that a 3-algebra is almost equivalent to a Z_2-graded Lie algebra (not a superalgebra). However, not quite, because the odd-odd-odd Jacobi identity is replaced by the “associative condition”, which says that the sum of two of the terms in the Jacobi equals zero. The tri-linear product is then the third term in the would-be Jacobi identity, and thus a Jacobiator.

    Hm. Or so I thought. Looking at eqns (47) and (49) again, it looks like I got some signs wrong.

    Sorry if this comment strays too far from the topic of the post.

  27. Looking at eqns (47) and (49)

    I read (48) as saying that the Jacobi identity holds everywhere except when you feed in three elements of curly A. On them it just plain fails. Not up to some Jacobiator.

  28. Observer says:


    The only reliable data on neutrino masses are the mass squared differences for solar and atmospheric neutrinos. Does the prediction of F-theory match these measurements?

  29. Peter Woit says:


    I don’t see a real prediction in the paper, and the authors don’t compare the numbers they quote to experiment, possibly since there is no way to do this. The vague neutrino mass scale in the paper is not inconsistent with what is known about neutrinos (e.g. mass differences), if it were the authors wouldn’t have pursued this.

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