A Prediction About a Prediction

In the years leading up to the LHC, string phenomenologists were vocal about their hopes to use string theory to make predictions about what the LHC would see, despite a history of a quarter-century of failure on the prediction front. For example, in late 2007 Michael Dine was writing in Physics Today:

A few years ago, there seemed little hope that string theory could make definitive statements about the physics of the LHC. The development of the landscape has radically altered that situation. An optimist can hope that theorists will soon understand enough about the landscape and its statistics to say that supersymmetry or large extra dimensions or technicolor will emerge as a prediction and to specify some detailed features.

The main target for a landscape prediction has always been what appears to be the simplest possible question about BSM physics that the landscape could hope to address: is the supersymmetry breaking scale likely to be high (GUT/Planck scale) or low (electroweak scale)? By the time the LHC data started to arrive (showing no supersymmetry), these hopes for a landscape prediction had failed, as it became clear there was no way to get a clear answer about this (or any other question…) out of landscapeology. Landscape proponents have still not given up though, with Michael Douglas yesterday putting out a survey of work on the SUSY question, The string landscape and low energy supersymmetry. He has no string theory predictions, but he has a (very tentative) prediction about a (sort of) prediction:

I am going to go out on a limb and argue that

String/M theory will predict that our universe has supersymmetry, broken at the 30 − 100 TeV scale. If at the lower values, we may see gluinos at LHC, while if at the higher values, it will be very hard to see any evidence for supersymmetry.

This is a somewhat pessimistic claim which far outruns our ability to actually make predictions from string theory. Nevertheless I am going to set out the argument, fully realizing that many of the assumptions as well as the supporting evidence might not stand the test of time.

As for the time scale and reliability of this prediction of a prediction, he writes:

My guess at present is that twenty years or more will be needed, taking us beyond the LHC era. Even then, it is likely that such predictions would depend on hypotheses about quantum cosmology which could not be directly tested and might admit alternatives. It is entirely reasonable that sceptics of the landscape should reject this entire direction and look for other ways to understand string theory, or for other theories of quantum gravity. At present we do not know enough to be confident that they are wrong. Nevertheless the evidence at hand leads me to think that they are wrong and that this difficult path must be explored.

So, optimistically, if all goes well, long after the LHC is shut down, maybe we’ll see a landscape prediction about whether the LHC should have seen SUSY. This prediction will depend upon assumptions about quantum cosmology that can’t be tested, so if it disagrees with what the LHC saw, that won’t falsify the landscape anyway.

Meanwhile, Gordy Kane is promoting the idea that string theory already has made a prediction: a 125 GeV Higgs mass, spectacularly in agreement with the latest data, and gluinos detected “by summer”, “with masses around a TeV, maybe less” (see here). He’s giving a talk today at the Simons Center with the title “String theory, the real world, and the prediction of the Higgs boson mass”. As far as I can tell though, no one except possibly his collaborators believes him. At a public talk on the Higgs recently here at Columbia, Brian Greene was very skeptical, joking that if the LHC had seen something at 142 GeV, that would be Kane’s “prediction” (for more about this, see Lubos’s outraged coverage here).

Matt Strassler recently weighed in on the Kane prediction, which so outraged him that he has stripped Kane of his professional title. Matt is careful to put “Professor” before his own name and those of others who deserve the title, but Kane is now “Mr. Kane”:

The level of garbage and propaganda surrounding the Higgs is getting pretty ridiculous.

You realize, yes, that by August 2011 the window for the Standard Model Higgs was down to 115 to 140 GeV, right? So your chances of getting within 5 GeV of the right answer is 15%. Many theories before Mr. Kane predicted a range that included 125 also. I’m completely unimpressed both by the science and the propaganda. Most of my friends who are experts in compactification (which Kane is not — he relies on one of his collaborators — and I am not an expert either) are not convinced of the assumptions on which they base their arguments. It all sounds good. But is it really? I’ve heard lots of arguments that sounded good over the years… and most of them are now known to be wrong. None of them are known to be right.

Do not judge science on the ability of the scientist (who wants his or her Nobel prize and is trying his or her best to convince you) to present a compelling argument. A great salesperson can create a terrific argument; a great physicist does not need one.

So, Kane seems to be finding that his “string theory prediction of the Higgs mass” is being met with scorn, from all segments of the particle theory community. I’m curious what has happened to his paper from early December, which I’d guess was intended for PRL, but has yet to appear. He has about a month and a half for the gluinos to show up “before summer” and vindicate his “prediction”.

The Strassler comment was at a useful posting about the state of SUSY searches (see here). Matt’s time estimate for how long it will take the LHC to rule out SUSY: “This will take a while, probably a decade.” A more mainstream time estimate might be that it has already happened. For Tommaso Dorigo’s take on this, see SUSY and the Silence of the (Roasted) Lamb.

Starting tomorrow Brookhaven will host a workshop on the state of SUSY topic. For latest developments, look at the slides as they appear here.

Update: The video for Kane’s talk at the Simons Center is now available. Instead of gluinos “by summer”, he’s now changed his tune, and he expects “discovery during 2012” (if the expected luminosity goals are met). The mass of the things has moved up from less than about 1 TeV to less than about 1.3 TeV.

Update: The Kane et al. paper with the Higgs mass “prediction” has just appeared at Phys. Rev. D. The preprint went to the arXiv on December 5, the Phys. Rev. D submission date is February 13. One guess would be that this more than two month delay might be due to the paper being rejected (or a referee insisting on the “string theory prediction” nonsense being removed) wherever it was first submitted, perhaps PRL.

This entry was posted in Uncategorized. Bookmark the permalink.

37 Responses to A Prediction About a Prediction

  1. Shantanu says:

    Great article, Peter. Btw what’s the status of models like Randall-Sundrum or ADD?
    From what I understand there is no evidence for these in LHC data. But some people such as Cliff Burgess(from his talk at PI) still seems sanguine. I asked this question to L. Randall when had a post on cosmic variance, but didn’t get a reply.

  2. Peter Woit says:


    LHC data has ruled out RS and ADD models at currently accessible energy scales at the LHC. Despite the huge publicity campaign for these things pre-LHC, hardly anyone ever seriously thought they would show up at the LHC. Now no one does, and it’s thought best to just try and forget the publicity campaign. In principle in a few years when the LHC goes to near design energy, there’s a new energy range to check. I seriously doubt though that even the biggest enthusiasts for these things would bet any money that something will show up, even with 10-1 odds in their favor.

  3. Allan Rosenberg says:

    “You realize, yes, that by August 2011 the window for the Standard Model Higgs was down to 115 to 140 GeV, right? So your chances of getting within 5 GeV of the right answer is 15%.”

    Last time I checked, 10/(140-115) = 40%.

  4. Bernhard says:

    Wow, so lots of people putting Gordy Kane in a tight corner. I think Witten should speak up too, that would probably put and end on his infamous campaign.

  5. P says:

    Hi Peter,

    Two questions, but first a comment.

    Mike Douglas is better situated to say things about the landscape than just about anyone, including predictions of individual vacua (they exist!) but also whether or not the landscape as a whole prefers certain types of physics over others (which would be interesting if it did, because quantum field theory doesn’t.) You make it seem that no one who is serious takes Kane seriously, but Douglas directly quotes Kane’s work as having influenced his thoughts on the subject.

    Which leads to my questions:

    Did you actually read the Douglas article or did you just cherry-pick the first section regarding “predictions”, bringing up the sorts of issues you usually do? That’s a fine approach to some articles, though still unfair, but Douglas is a real expert and he wouldn’t put his name on it without serious thought. There are very few people on the world that have his level of knowledge on string vacua and the landscape.

    And a more playful question:

    It seems you’re not a fan of low energy SUSY. Do you believe that Higgs boson exists, and if so, what is your favorite mechanism for solving the hierarchy problem and why? Many theorists would invoke SUSY for precisely that reason.


  6. Slacker says:

    The paper of Kane et al clearly states all the assumptions and caveats, e.g. the MSSM spectrum below the GUT scale, N=1 D=4 supergravity framework, etc, so I see no reason for Mr. Strassler to belittle this work and refer to is as ‘garbage’. Btw, both Acharya and Kane were twice acknowledged in the Douglas paper, so string phenomenologists do pay close attention to what they have to say. If you read their most recent review and compare it to the Douglas paper you’ll notice a common thread. The set of arguments presented in their review, which also includes the Higgs mass discussion, are not at all controversial and pretty much agreed upon by most string phenomenologists who understand the details of moduli stabilization and SUSY breaking in N=1 D=4 supergravity.

  7. Peter Woit says:


    Perhaps you can take up Strassler’s and Greene’s evaluation of Kane’s claim with them. I’d be curious to know if you can find a single prominent theorist (not a collaborator of Kane) willing to say publicly that he thinks Kane really has done what he claims: predict a Higgs mass of 125 GeV from string theory.

    Slacker and P,

    I don’t doubt that Douglas has paid attention to what Kane is trying to do, and, as he says, that line of thought has influenced his hopes of getting predictions out of string theory. I also note that he doesn’t reference Kane’s December paper claiming the 125 GeV prediction, or mention this prediction. He’s quite explicit about what he sees as prospects for getting predictions out of string theory, and what he says about this is completely inconsistent with Kane’s claims. He is clearly implicitly saying he doesn’t believe that Kane has a string theory prediction of the Higgs mass.


    I read parts of the paper carefully, skimmed others enough to see what arguments Douglas was making. Note that I’ve attended several talks by him on this topic, read the slides of others, as well as several of his previous papers. With this background, I looked at his paper to see what was new. The most striking new thing to me was the much more pessimistic evaluation of prospects for this program, so that’s what I wrote about. I’ve never heard him before say that it would be at least twenty years before this led to any sort of prediction, and that even then it wouldn’t be a real one (i.e. you would always have to put in assumptions about string cosmology).

    Kane I think is really out of his mind, making absurd and outrageous claims. Strassler’s “garbage” quote is apt. Douglas is quite different. He’s not claiming to have solved any problems or to have something he doesn’t have. He even acknowledges that others looking at the same set of facts as him will quite reasonably conclude this is a doomed project.

    I’ve repeatedly written about the “hierarchy” problem here. My basic point of view is that I’m unconvinced that it’s a problem. One way of stating the problem is to say that we have no explanation for why the electroweak scale is so small compared to the GUT or Planck scale. Here I think it’s a good idea to keep in mind that we don’t even know if there is a GUT scale, and don’t know enough about quantum gravity to understand the significance of the Planck scale. Put differently, the hierarchy problem is largely a problem set inside the GUT/string scenario of what a unified theory looks like. Such scenarios seem to so far be failures, so why worry about a “problem” that comes with them?

    The Higgs field does pose serious problems, but they seem to me different than the “hierarchy” problem. Matter and gauge fields have a geometrical structure that tightly constrains their behavior. A scalar Higgs doesn’t, introducing for instance the highly undesirable feature of completely unconstrained Yukawa couplings and thus arbitrary fermion masses and mixing angles. This to me is what really cries out for explanation, not the fact that the Higgs mass is small compared to the Planck scale. If SUSY had anything interesting to say about that, then I’d be a fan.

  8. Shantanu says:

    Peter or others, I think someone mentioned on physicsforums that Wetterich and Shaposhnikov had a paper on Higgs mass of 125 Gev 2 years before CERN result
    (see http://arxiv.org/abs/0912.0208). What do you think of this
    Why doesn’t anyone refer to this or mention it as a prediction of “string theory”?

  9. Peter Woit says:


    I know nothing about that particular calculation, but it is remarkable that the Higgs is in the range where the SM holds out to very high energies. But, since this has nothing to do with string theory, it doesn’t get that much publicity.

  10. theoreticalminimum says:

    I think it might be somehow interesting to some to read some of the other articles to figure in the memorial volume, which are linked to here.

  11. Andy says:

    Higgs-mass predictions, by Thomas Schucker
    gives a list of 96 Higgs-mass predictions, with references.

  12. M says:

    It is beautiful to see how well these pre-dictions change when new data arrive.
    We should admire how flexible is string theory in adapting to whatever experimental result, improving from old-fashioned Heterotic Strings to modern Elastic Strings.

  13. theoreticalminimum says:

    I am currently watching the linked Kane talk. First of all, I am very surprised that Kane spent so much time painfully elaborating so much on what would be considered very elementary to a SCGP audience. Did he realise he was talking to experts in theoretical physics? Just something that caught me off-guard: I’m not sure I understand what Kane meant by F=ma not being testable. He used the word “tested” many times in his talk, but didn’t seem to be bothered to define what he understands by something being testable or not. Can anyone enlighten me?

  14. piscator says:

    The simplest objection to the Kane etc work is that G2 manifolds are not, unlike Calabi-Yaus, actually constructed. The `G2-MSSM’ does not involve an actual construction of the MSSM and does not involve an actual G2 manifold.

    So given that in the UV you don’t have the manifold and you don’t have the model, many (including myself) think a little humility is needed on the the extent to which any of this work represents string theory predictions for the Higgs mass.

  15. Bernhard says:


    you mean “about 1 *TeV* to less than about 1.3 *TeV*”.

  16. Peter Woit says:

    Thanks Bernhard, fixed.

  17. Bernhard says:


    I also don´t get it. Kane say other strange things like “the Standard Model is the most theoretical theory that´s ever been, maybe that ever will be”, but none of them is more nonsense than

    “last summer we did a string theory, a honest string theory calculation of predicting the Higgs boson mass and the one they reported in December was the one we predicted they should report”.

  18. Peter Woit says:


    This is now standard issue string theory ideology: string theory (which predicts absolutely nothing) is just as good as the quantum field theory (which gives us the Standard Model, the most successful theory in the history of science). The argument is that both are just “frameworks”, just like “F=ma” is a “framework” (you need to pick a QFT, and pick an F, just like you need to pick a “string theory vacuum”).

    Arguing that the biggest failure in history of science is the same as the biggest success is obviously sophistry, but rather popular sophistry these days.

  19. Mark says:

    piscator, indeed, the G2-MSSM does not involve a specific singular G2 “manifold” (explicit smooth examples have been constructed by Joyce and Kovalev and the singular ones should exist by the arguments involving dualities) but instead, it uses the most general *known* properties of G2 manifolds. The scaling dimension of the 7-dim volume wrt to the moduli is known, the form of the moduli Kahler potential is known from dim reduction, likewise, the general functional form of the gauge kinetic function in terms of the moduli and the general dependence of the Yukawa couplings on the moduli are known, and the general scaling properties the Kahler metric for bifundamental chiral matter is also known from locality. It turns out that one can robustly demonstrate how to stabilise the moduli in this very general case without referring to a specific G2 construction, for instance, without knowing the precise moduli dependence of the volume in the Kahler potential but only its scaling property. Also, surprisingly, it turns out that the soft breaking terms in these vacua “forget” about most of these microscopic details as these computations involve a bunch of contractions, so the explicit moduli vevs drop out of the final result. In the end, the only moduli dependence appears through the 7-dim volume, which is considered a parameter, but which becomes fixed from bottom-up by the relation between alpha_GUT and m_planck. The specific properties of G2 manifolds that directly affect the numerical coefficients in the final results for the soft terms are the scaling dimensions, which are known. Be assured that Bobby Acharya, who is a world expert in these matters, would not be putting his name on these papers if there was something dodgy.

  20. Mark says:

    piscator, here is the G2-MSSM reference I found to be the most useful: http://www.springerlink.com/content/g6288v55tj184588/?MUD=MP

  21. P says:


    Forget the F=ma stuff.

    You state that you don’t the like argument but you don’t actually argue against it, which particularly frustrates me because I’ve espoused this view multiple times.

    String theory and quantum field theory make predictions about the sorts of objects that exist in those frameworks. Neither, as frameworks, makes precise predictions about precise structures.

    A string vacuum or a particular quantum field theory require introducing more input. Each makes precise predictions (matter content / gauge symmetry and scattering amplitudes, e.g.) that either are like the world or are not like the world. Most string vacua look nothing like the standard model. Most field theories look nothing like the standard model.

    It is dishonest and an outright lie to pretend like an individual string vacuum doesn’t make precise predictions about things like gauge symmetry and matter content. The ST FT and string vacuum particular QFT analogy is a good one for the reasons just mentioned. The issue, as I say over and over, is whether or not with LOW ENERGY EXPERIMENTS we can tell the difference. After all, at low energies, string vacua just look like effective field theories.

    It’s not that there aren’t issues – there are – but pick the right ones, please. The landscape and the vacuum selection problem are the issues, not whether individual vacua make predictions.


    P.S. Your previously comment about the Higgs mass hierarchy problem misses the point that it doesn’t require GUTs or strings. The problem is the fine-tuning associated with the quadratic divergence of the Higgs boson mass, which has nothing to do with WHAT the UV completion is.

  22. P says:

    I second what Mark says.

    Agreed, the big drawback of the G2-MSSM scenario is that no one has constructed an actual global MSSM model of M-theory on a G2 manifold.

    Their scenario takes a very different approach, as discussed by Mark.

  23. P says:

    Sorry to harp, Peter, and sorry for three postings in five minutes.

    Just to remind everyone, by the “biggest failure in the history of science”, Peter is referring to string theory for the purposes of unification and a theory of everything.

    Though I find his arguments flawed, there, as do many, I think that he and I would both agree that string theory as a subject has made tremendous contributions to pure mathematics and our understanding of quantum field theory, regardless of any statement about unification of fundamental physics.


  24. Peter Woit says:


    I’ve repeatedly, many time, here explained what I see as the difference between the Standard Model situation and the string theory vacuum situation. In one case, among the simplest possible choices leads to an extremely restrictive and predictive model, one that makes absurdly precise predictions, which agree exactly with experiment. In the other case, all you are doing is cooking up more and more complicated models, carefully designed to avoid falsification.

    Trying to argue that the QFT/SM situation is “the same” as the string theory/string vacuum situation is like trying to claim that black=white, since they’re both shades of grey. It’s a waste of time to try and have a discussion with someone who wants to tell you why black=white.

    About the hierarchy problem: the quadratic divergence may just be an artifact of perturbation theory. I state it the way I did (which is quite conventional) because it makes sense non-perturbatively.

  25. Bernhard says:


    I think the problem is in in the framework itself. To put differently, what do you need to construct a realistic theory of nature starting from QFT and starting from string theory? Peter made some interesting comments e.g. here: http://www.math.columbia.edu/~woit/wordpress/?p=4065&cpage=1#comment-98564

    And after we deal with this very ugly construction, what does it predicts? At low energies you say it looks like QFT, so I certainly don´t need it.

    At high energies (GUT scale? Planck?) what does it say? Would one be able to compare string theory with experiment in the same way the standard model is, even if we had a galactic accelerator?

    I don´t think so, put please correct me if I´m wrong.

  26. piscator says:

    Mark, P

    Thanks for the comments. I do know this model and these papers (in fact I was the referee for the paper Mark referred to).

    It is a perfectly well-defined and honest task to take a 4d supergravity model, with assumptions that are more or less inspired by string theory, and study its properties and analyse its phenomenology. The model considered has some interesting features and it is perfectly reasonable to study it.

    However this gives absolutely no justification for saying this is a string theory prediction of the Higgs mass. I haven’t watched the video, so I don’t know whether the quote is accurate, but it is indefensible to call this an `honest string theory calculation’.
    This is not string theory. At best it is a 4d supergravity theory with properties inspired by string theory – which is fine, but is not string theory.

    String theory is special because of its ultraviolet behaviour. Look at the ultraviolet for these models – there is no actual manifold there, there is no actual construction of the MSSM, there is not even the worldsheet picture as you are in the M-theory regime.
    I’m not that down on this, because the subject is hard and you have to do what you can and not what you can’t. But let us be honest about the difference between computing something and postulating it.

  27. P says:


    Simplest possible choices!? The representation theory and couplings of the standard model are far from simple.

    And remember, I’m not comparing vacua with the SM, i.e. a single field theory. I’m comparing vacua with particular QFTs. The point is, given a particular quantum field theory or a particular string vacuum, in each case we can ask “does this match what we see in the world?”. We have a particular quantum field theory, the standard model, that experiment tells us correctly describes particle interactions below the TeV scale or so. It has a tremendous amount of unpredicted, empirically determined input. Tell me, now, what predicts the tremendously detailed, complicated structure of the standard model? What predicts the gauge symmetry, matter content, and chiral structure? Because string vacua predict these things, remember . . .

    Re the hierachy: okay, I’ll agree with that, but it’s still not a GUT / string issue. It’s a “high scale” issue. Any non-perturbative physics which would solve the hierarchy problem would have to kick in at a very low scale (TeV), though. And your point is that it would alleviate the quadratic divergences and cut off the running?


    Thanks for the comment. Your question “why do I need it?” depends on your taste. If you’re just interested in modeling nature at low energies and are fine with unexplained mass hiearchies (note: different from previously discussed hierarchy problem), e.g., then effective field theory will model it just fine. String vacua give many mechanisms for explaining detailed structure and also predict things that QFTs don’t (as far as I know): gauge symmetry, matter content, and chiral structure.

    At high energies, there definitely are stringy signatures that are clearly distinguishable from field theory. Technically this occurs at the string scale, but this is typically a high scale near the Planck scale. There, it is possible to excite very massive string modes which form an infinite tower, and there are papers on how the collider signatures could determine that it is a string mode and not some other type of tower of modes, such as a KK mode. It’s worth pointing out that, along with gauge symmetry (almost always spontaneously broken) and general relativity at long distances, such modes are generic predictions of all string compactifications (that I know of). It is on the details where particular vacua differ, such as the precise structure of the gauge theory, and these are very important.

  28. P says:


    The one addendum is that their “string-inspiredness” regarding moduli masses really is applicable to all string compactifications. How broadly their claim about m_3/2 holds in M-theory, I don’t know.

    I couldn’t agree more. Very well said. Thanks for the comment.


  29. Peter Woit says:

    In the case of string theory you’re invoking a non-existent fairy land, where all the many problems of string theory and string theory “vacua” have vanished. In the case of the SM, you’re describing a theory that can be written on a t-shirt as “tremendously detailed, complicated structure”, and the trivial and defining representations of SU(3) and SU(2) as “far from simple”. This kind of argument allows you to equate black and white, but it’s kind of absurd.

    Again, I’m not convinced there is a hierarchy problem that needs to be solved. The quadratic divergences are not obviously relevant. Until you have some specific kind of new physics at a higher scale, you just don’t know whether the fact that the electroweak scale is much smaller than that scale is something that requires any explanation.

  30. Mark says:

    piscator, I agree, these are effective N=1 D=4 sugra computations where W, K and f are dictated by the known properties of G2 manifolds/compactifications. I’d also add that apart from toroidal orbifolds where explicit worldsheet computations have been done to compute, e.g the moduli dependence of the Yukawa couplings, Kahler metric etc, a lot of string phenomenology comes down to an effective field theory analysis combined with methods from algebraic geometry. I’m convinced that a lot more progress would be possible if explicit global G2 examples were constructed, independent of whether we have a complete formulation of M-theory. So yes, I think that for Gordy Kane to claim that they did explicit string theory computations is very misleading but. having seen his talk, I’d say go easy on him, he is not a string theorist so maybe he just does not know the difference, but his enthusiasm is certainly inspiring.

  31. P says:

    @ Peter:

    Name a particle in the standard model that is only in the fundamental of SU(3) or SU(2) and transforms trivially under all other groups. Give me an example of some trivial structure of couplings or mixing angles that appears in the standard model.

    The only reason we have identified the standard model as a good description of nature is because low energy experiments are good at distinguishing between particular quantum fields theories in the continuously infinite class of theories. The real problem with string vacua isn’t that they don’t make predictions. The problem is the landscape, and the fact that at TeV scale energies string vacua almost always look like standard quantum field theories. Sufficiently high energy experiments would be able to not only distinguish between the effective theories of different vacua, but also differentiate between whether nature is described by a string theory or a quantum field theory which is UV completed in a different way.

    You’re not really even responding to my arguments and instead are just saying the names of colors and invoking fairies. Please, please, please: just acknowledge the real problem. A string vacuum makes predictions, e.g. a low energy gauge theory. Almost none of them look like the standard model, but some do. With low energy experiments, it may be impossible to decipher which UV completion gives rise to the effective theory that describes nature. That is the problem, not that a string vacuum doesn’t make predictions. If you acknowledge this, I’m happy to stop harassing you, but I feel the need to respond as long as there are false things stated in these comments!

    You are not a string theory expert and have written a popular book and gained a voice in the community – and there should be dissenting voices, including yours – but progress of science requires honest dialogue about what the problems actually are in any given field. You seem to miss the actual problems, sometimes. Notice that I’m not one of those string zealots who is trying to say there aren’t problems. I’m just trying to be clear about what they are . . . and I’ve stated them here.

    Q: Do you acknowledge that a given string vacuum predicts the low energy gauge group and matter content? You continually avoid this question and imply that a string vacuum makes no predictions. Maybe you’re just not aware, but I’m curious.

    Regarding the hierarchy, I’m confused by what you’re saying. Are you arguing that there isn’t a fine-tuning problem between the bare mass and the lambda^2 contribution? Surely that must not be it – I’ve never heard a physicist take this viewpoint – but if so, please explain. The fine-tuning problem is independent of what new physics might come in at the cutoff.

    @ Mark: right on.

  32. Peter Woit says:


    Yes, there are 3 couplings in the standard model we don’t understand the origin of, as well as an interesting, simple, pattern of representations of SU(2), SU(3) and U(1), involving nothing more complicated than the fundamental representations in the case of SU(2) and SU(3). This is a very small amount of basic data we don’t understand and have no idea what explains it (best effort is the SO(10) GUT). There’s also a matrix of masses and mixing angles, and two couplings, all due to the Higgs field. That’s a huge problem we have no idea about.

    For the case of string theory: we don’t even know what string theory=M-theory is, and we can get almost anything we want out of it. No one has any way of even saying what a “generic” string theory/M-theory vacuum would be, or, given best guesses of such a thing, no way to reliably calculate what it predicts. The one “M-theory vacuum” that has been extensively studied outside of perturbation theory (AdS5) looks nothing at all like the real world: wrong dimension, none of the SM at all). All “string theory vacuum predictions” are based upon going to some extreme limit of parameters where you hope string perturbation theory will be reliable and various assumptions about branes will work out, and engineering something to fit the simple data that define the SM. When you do this, all you ever get is what you put into it.

    I have no idea who you are and whether you have any idea what you are going on about. The description I gave above of the situation of string theory is not just my opinion (based on 30 years in this business), but now conventional wisdom among particle theorists. Even most string theorists these days agree that string theory can’t be used to predict anything and think activity like Kane’s is a bad joke (see the Strominger talk linked to in the next posting for example).

    Answers to your questions: as explained above, you only get reliable calculations of the low energy field content when you drive the theory to a corner of its parameter space, and make some optimistic assumptions. As for the hierarchy problem, for the N’th time, the problems with the perturbation expansion is not obviously a physical problem. I don’t have time to find a good reference that explains the standard lore about this, but 5 seconds of Googling turned up this paper


    which explains the issue from the point of view I’ve been talking about, one which is completely conventional.

  33. P says:


    We’re in complete agreement, then, about how the standard model is complicated, particularly at the level of Yukawa couplings which all involve the Higgs field, and how the matter content representations fit nicely into the 16 of SO(10). We’re also in agreement that this is a huge problem, and you would probably agree with me that it would be tremendous progress in particle physics if one were able to derive them from some more fundamental consideration.

    Since you mentioned how SO(10), for example, can nicely explain the standard model representations, I’ll mention how this might arise in one type of string vacuum, though similar considerations hold elsewhere. Consider heterotic M-theory on CY3 x interval. This is not simply a “region” of “parameter” space (which doesn’t even make sense, we should be talking about moduli space). A stable holomorphic bundle with structure group SU(4) will break the E8 (which must exist at 1 end of the interval for anomaly cancellation) directly to SO(10). Simple discrete choices of bundle-defining parameters can give rise to 16’s of SO(10). As you implied by your mention of SO(10), all of the standard model fermions can fit into this representation. Furthermore, a good deal is known about non-perturbative effects in heterotic M-theory (worldsheet instantons and the like), contrary to what you implied. So getting things something like the standard model reps are definitely NOT just in miniscule regions of parameter space where all we have is perturbation theory and we don’t know anything else.

    Rest assured that I am well educated in both particle physics and string compactification and am familiar with the pitfalls and subtleties in both subjects. I am someone who sometimes feels the need to correct misinformation about these subjects on the web, regardless of where it may be. Often times I see it on this blog. Regarding particle theorists, many dislike string theory for the sake of unification. Sometimes that dislike is out of knowledge (as I’ve said, there are good criticisms!), and sometimes out of ignorance. Then there are also serious particle physicists who like string unification and have worked on it or related topics.

    Regarding string theorists themselves, many would probably be wary (as would I) of the ability of low energy experiments to determine the UV completion of the effective theory we see at low energies – i.e. to test the stringiness of string theory that is not present in QFT. But 95% of string theorists would tell you 1) that string vacua predict certain things at low energies such as gauge symmetry and matter content (as evidenced by quality of people in the last ten years who have worked on these things) and 2) at high energies (string scale) there are clear stringy signatures that would allow one to distinguish between string theory and quantum field theory. This is a limitation of our experiments, not of our theory.

    Regarding hype, we’re in total agreement. It has no place in any science of any kind, and honest dialogue about science is the only proper thing to replace it.

    Regarding the hierarchy – perhaps there is something I’m missing and I should look at this paper closely. But as an expert it worries me that I’ve never heard of the people who wrote that paper, and moreover I’ve never heard any particle theorist try to dismiss the hierarchy problem in the way you are. An alternative Google search “why the hierarchy problem is a problem” returns two Wikipedia articles first, and then some slides by Joe Lykken on solving the hierarchy problem. He, a very very well known particle theorist, as you know, seems to take it quite seriously.

  34. P says:

    clarification: on the last paragraph, I mean that as an expert in high energy theory (not the hierarchy problem) who very often talks to people who focus solely on particle physics, I’ve never heard anyone try to dismiss the hierarchy problem in the way you are. Humbly, I haven’t thought about it too seriously beyond the common objections stated by particle theorists. There may be more things to take into account that I’m missing, but my point is that very very good people take the problem very seriously and don’t just talk it away. I’ll take a look at the paper you posted this week, though.

  35. Peter Woit says:


    Yes, I know you can get SO(10) and the spinor rep (as well as just about anything else…). The big problem though with an SO(10) GUT (besides proton decay, or course…) is that you don’t have a good idea about how to break it down to the SM. Adding more Higgs fields just adds a new set of parameters you don’t understand in addition to the SM ones. If string theory provided any insight into these problems it would be interesting, but it doesn’t. The problem with string theory, right back to 1984-5, is that it doesn’t tell you anything about the SM you didn’t already know. This was the reason I (and many others) were skeptical about the whole idea from the beginning. Nearly 30 years of effort hasn’t improved the situation, quite the opposite.

    The paper I linked to was randomly chosen, I don’t know the authors. Their introductory text though makes clear that they are just repeating conventional wisdom you can find anywhere. This is the way the “hierarchy problem” looks if you try and state it non-perturbatively. As for my point of view on the “hierarchy problem”, maybe it is a minority one, but I think if you ask around you won’t have trouble finding theorists who were never impressed by the “hierarchy problem” argument, or see it as a relatively weak one, tied to our flimsy ideas about GUT-scale physics. The idea that there is a GUT/Planck scale and that you should worry about it is certainly part of the standard lore of how to think about BSM physics, but this lore has been highly unsuccessful in terms of leading to anything.

    Much of the attention to the “hierarchy problem” was always because of its use as an argument for why the LHC should see BSM physics. Now that this physics is not showing up, the “hierarchy problem” argument will start to get ignored.

  36. Anonyrat says:

    1. If String Theory cannot tell me anything about how the effective QFT GUT (e.g., SO(10)) that it yields further flows down to the Standard Model, then the solution of the mystery of the Yukawa couplings and of the hierarchy problem (if there is one) cannot lie in String Theory.

    2. For String Theory to be convincing as a lead I would want to follow, at a minimum, I would expect the stringy SO(10) GUT to be very strongly theoretically constrained. It should pick a very tiny part of the space of SO(10) GUTs that can plausibly flow down to a low energy theory that looks like the Standard Model. If it does that, even if I can’t practically calculate anything, I’d be strongly inclined to take another serious look at String Theory.

  37. P says:

    Hi Peter,

    Sorry for the delay in writing back, it’s been a busy week.

    Regarding your SO(10) comments – I don’t disagree quite as much with these, though I’m certainly no expert on Higgsing it to the SM (126-dim rep, right?). There has been some talk of whether these reps are even possible in string vacua. A rough argument against them is that in many types of string vacua, a 248 of E8 is the highest rep, so you’re not going to get a 126 of SO(10).

    A string vacuum can and does predict things that QFT does not, e.g. particular matter reps, etc. If one vacuum was uniquely selected by some mechanism (hopeful), this would be a prediction (or postdiction, you might say) of something that is input in the standard model. But barring that, it is likely very difficult or impossible at the TeV scale to differentiate whether the effective field theory we observe is lying in a string vacuum or some other UV completion. Though you might not be happy with the first two sentences, I bet you’d happily agree with the last.


    Certain it is well known that string vacua do give mechanisms for accounting for Yukawa hierarchies and the like. Small Yukawas can be generated radiatively from bulk effects or from any of the myriad of instanton effects, for example. There are also various rank arguments in F-theory.

    The space of SO(10) GUTs is enormous, but gauge theories in string compactifications are typically more constrained than the space of all gauge theories due to something known as tadpole cancellation. For example, in QFT you could take SO(10) GUT with N 16 dim spinor reps. Quantities like N are typically bounded in string compactifications. In QFT they are not. Of course, from data observed below a TeV, N=3 seems like the right number, but we do not know for sure.


Comments are closed.