There’s a very interesting new paper on the arXiv by Joe Polchinski, a survey article for Studies in History and Philosophy of Modern Physics, entitled just Dualities. It’s an unusually lucid summary of the story of dualities in quantum field theory and string theory. This is a very complex subject which has been a central one in theoretical physics for the last few decades, but most expository writing on the subject has tended to be either superficial promotional material or mired in technical detail obscuring fundamental issues.

One reason for this is that, as Polchinski does an admirable job of making clear, in a very real sense we still do not understand at all the fundamental issues raised by these dualities. He notes that “we are still missing some big idea”, and points to the same comments from Nati Seiberg last month that I blogged about here. For most of the dualities at issue, our current standard technology for dealing with QFTs (the Lagrangian and the path integral over classical fields) is capable of capturing the two QFTs that are in some sense “dual”, but we lack a viable larger framework that would give the two QFTs in two different limits and explain the duality relationship.

For an example of the problem, probably the oldest and most well-studied case where we are missing something is Montonen-Olive duality, a non-abelian duality between electric and magnetic charges and fields. A currently popular idea is to find the explanation of this in “Theory X”, a 6d superconformal QFT, with duality coming from compactifying the theory on a torus (for more about this, see talks last week in Berkeley). The problem with this is that we don’t have a definition of the “Theory X”.

Polchinski places this problem in the context of a conjectural “M-theory” with various string theory limits. This has been the dominant idea in the subject for nearly 20 years now, but we seem no closer now to finding an actual realization of this conjectural picture than we were back in the mid-90s. Twenty years and thousands of papers have just given better understanding that various possible ideas about this don’t work.

One place where I think Polchinski’s survey is weak is in the treatment of this conjecture, where at times he takes as solid result something highly conjectural. For instance he starts off at one point with:

String-string dualities imply that there is a unique string/M-theory.

and moves on to the conjecture that

In this sense it may be that every QFT can be understood as a vacuum state of string/M-theory.

The problem here is that he’s built a speculative view of the unification of physics, constructed on an assumption about a “unique” theory, when we don’t know at all that such a thing exists. One basic lesson of mathematical research is that you need to keep very clear the distinction between what you really understand and what is speculation, because your speculation is often wrong and if so will lead you in the wrong direction. I think particle theory of recent decades likely suffers from people forgetting that some ideas are speculative, not firmly grounded, and may be pointing in the wrong direction.

One wrong direction this takes Polchinski is to the non-predictive, pseudo-scientific landscape of supposed string theory solutions and the multiverse, which he blithely invokes as our best fundamental explanation of physics. Tellingly, unlike the clear explanations of other topics, here he makes no attempt to describe these ideas other than to note that

they rest on multiple approximations and no exact theory.

In a final section, Polchinski addresses the question of what all this tells us about what is “fundamental” and what is the role of symmetries. This is the crucial question, and I’d argue that our lack of understanding of where these dualities come from likely is due to our missing some understanding of how symmetries are realized in QFT or string theory. This has been the lesson of history, with the Standard Model only coming into being when people better understood how symmetries, especially gauge symmetries, could act in QFT. Polchinski largely takes the opposite point of view, arguing that the fundamental theory maybe has no symmetries, local or global. He quotes Susskind as suggesting that symmetries have nothing to do with fundamental equations, are just calculational tools for finding solutions. I think this is completely misguided, that a strong case can be made (and I do it here) that “symmetry” (in the sense of the mathematics of groups and their representations) lies at the very foundation of quantum mechanics, and thus any quantum mechanical theory, even string/M-theory, whatever it might be.

Wondering whether there will be an arXiv trackback to this, and whether Polchinski has something to say about it…

Update: The arXiv Monday evening has a large collection of excellent review articles entitled “Exact results on N=2 supersymmetric gauge theories”, edited by J.Teschner (first is arXiv:1412.7118, last arXiv:1412.7145). Some of the results reviewed are based on deriving implications of the existence of the 6d (2,0) models discussed here and in the comment section.

Update: I’ve put this blog posting in the Multiverse Mania category, not because of the posting content, but because of comments in the comment section from Polchinski and Bousso.

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61 Responses to Dualities

  1. Peter Woit says:

    I disagree with many of your claims, e.g. that I have no scientific argument that string theory does not work, but the issue at hand is the arXiv policy. You don’t seem to know what it is any more than anyone else. I think if you follow most trackbacks to the arXiv you’ll find that very few of them are to the kind of technical discussion that I’m supposedly not providing.

    I think you do though get at the reason the arXiv is doing what it is doing, and Polchinski’s behavior also makes this clear. People don’t like criticism, especially accurate criticism, and a decision has been made to ban trackbacks to my blog because of its critical point of view about a certain scientific research program.

  2. Sesh says:

    I am a working physicist, and I write a blog that refers to arXiv papers. Trackbacks from my blog do appear on the arXiv (not that it makes much of a difference to me whether they do or not, my blogging software sends the trackback links automatically). With that context out of the way, I have the following observations:

    1. The arXiv includes trackbacks from a number of “journalistic” sites that contain no serious technical discussion, such as the Atlantic (clearly a departure from the trackback policy as stated in 2006).

    2. The argument that to be included in trackback lists blogs should contain “actual science content” is not just obviously not current arXiv policy, it also appears unworkable. Are there any blogs that do this? If I have something that constitutes “actual science content” (i.e., an original research paper), I put it on the arXiv direct, not on my blog. Surely blogs invariably contain only the “meta signal” of science discussion, criticism, opinions, news etc. irrespective of their technical level or whether the author is an active researcher or not.

    3. Bearing the above point in mind, when I follow trackback links from the arXiv – which I only rarely do, and only for papers outside my field of expertise – I do so precisely because I want to read a less technical (or even non-technical) discussion about the paper in question, including possible general criticisms. The primary literature is already there on the arXiv in the form of the actual papers, when I follow trackback links I am specifically looking for secondary literature. To me this seems to be the main point of trackbacks.

    4. The signal/noise ratio of any blog is also a function of the quality of the comment threads. This blog seems to have a very high readership from among practising physicists, and therefore a far higher standard of discussion in the comments (whether or not they agree with the original posting) than almost any other science blog I know of.

  3. NumCracker says:

    Dear Dr. Woit,

    AFAIK string theory was able to derive Black Hole area/entropy relations from first principles and, from a numerical perspective (at equivalent rigor level as taken by lattice QCD theorists) it nonperturbatively implies on a 3+1 world like ours (http://arxiv.org/abs/1108.1540). So in my humble perspective, it is not the theory that is “Not Even Wrong” … but the ability of modern physicists to analyse that from the numerical side that is still too naive.


  4. Peter Woit says:

    While the general issue of “is string theory not even wrong?” is off-topic here, the specific model you mention is discussed by Polchinski in his “Dualities” paper. There he writes about the sort of Matrix theory you mention

    “One challenge that remains here is that if one compactifies some of the dimensions (to get down to the four noncompact dimensions of our vacuum), Matrix theory becomes complicated, and if more than three dimensions are compactified its form is not known.”

    About the specific matrix model you discuss, he writes in a footnote:
    “There is a covariant form of Matrix theory, based on ten Matrices X^u, which is supposed to describe IIB string theory [46]. However its full interpretation is not clear. One issue is that time, which is one of the ten matrices, must be Euclidean.”

    I don’t believe that that it’s accurate to say that the theory is as well defined as lattice QCD, or that the issue here is just not big enough computers.

  5. Raphael Bousso says:

    Thanks for the various responses to my earlier comment. Some readers took offense at my suggestion that folks don’t read this blog because Peter’s opinions are founded in deep technical expertise; yet the very same posters went on to explain that indeed, they come here for different reasons. I, too, visit regularly; the site is well curated and has useful links. (I even recall taking advantage of a funding opportunity that I might have overlooked had it not been condemned on these pages.) But let’s not mistake the services and the discussion offered here with scientific research, as Peter does in asserting that his blog “contains science”.

    Doing science at any robust level does require a high degree of technical competence, along with other skills. This is what makes progress slow and hard-earned, much unlike the opinions voiced on blogs. The two papers referred to earlier illustrate this well. They engage in the presentation and analysis of a technical question that is of some interest beyond the string landscape, so no excuse for reflectively dismissing them. The question also bears on the validity of the KKLT construction.

    Peter admits he has not made an effort to follow. Yet, as he notes, the validity of some construction of this type is central to his criticism of string theory on the grounds that it has many vacua. This is only the starting point of his many confident declarations about the subject; yet he concedes he has no real understanding of the case for or against its validity.

    Rigorous criticism is what drives science; but simply jumping to a poorly founded conclusion and holding onto it independently of any developments is not rigorous criticism. After evidently taking our claim that string theory has many vacua on hear-say, Woit goes on another leap to conclude that therefore the theory is unpredictive and hence unscientific.

    I know much less than Peter thinks he knows, so I have no pat conclusions to offer. One thing I know, from actually trying, is that it’s a lot harder (but not impossible) to work out predictions in string theory than it was for the Standard Model, which also has a lot of solutions. (This is largely because we can test the Standard Model directly at the energy scales where it is simple—we don’t have to infer the Higgs mass from an eV scale experiment. In quantum gravity, we expect the theory to be simple at the Planck scale, and if someone could access that scale there would be plenty of predictions to check.) But Peter isn’t merely saying that progress is too slow, and the connection with experiment too difficult to establish, for quantum gravity research to be worth anyone’s time—a legitimate if radically defeatist position. He simply knows that string theory is not science. Maybe he knows more than I do, but his response to my comment does not give me great confidence.

  6. Peter Woit says:


    A few quick comments before I’m off to holiday celebrations:

    1. I’m glad you’ve found information here useful!

    2. About KKLT, etc. No, I’m no expert on validity of the approximations used. I have though paid close attention (and often written about on this blog) to papers which try to get actual predictions out of such scenarios. As an example, attempts to decide whether this predicts high or weak-scale SUSY breaking. This effort convinced me that there was no plausible vision for this working out. Others may disagree, and they should keep working at this if they want, but I think it’s a fair assessment that the past ten years have not been kind to such efforts. In recent years I see few serious attempts to make predictions, replaced by a lot of experts instead just assuming that, if these things work, they have very little predictive value and then, instead of abandoning the ideas, saying that, well, nothing we can do, that’s how nature works. This seems to me a serious problem for the field.

    2. I’ve never said “string theory is not science”. String theory is a huge subject, with all sorts of science going on, and some mathematics. Even KKLT is science, but it’s failed science. Once you come to the point where it becomes clear that your favored idea about nature has led you into something very complicated, with no positive evidence for it, and lots of evidence that the idea is unpredictive, the scientific method says you give up and do something else. Refusing to do this and instead asking for a change in the scientific method is the problem, and the point where the subject turns from science into pseudo-science.

    3. Sure, maybe my evaluation is wrong, and people will find some way to turn this back into science. From everything I’ve seen, that’s not happening though, with things headed in the other direction.

    I think it should be clear to all where we disagree and are making different judgments, and future developments may make clear whose were better. So far, when I look back at what I was writing about this a decade or more ago, I think that writing holds up well.

    Anyway, off to holiday dinner, best wishes to all, whatever their views on KKLT and the multiverse….

  7. NumCracker says:

    Dear Dr. Woit,

    I am not telling that such matrix models are at the same foot as QCD, actually they have no fermionic sign problem on the lattice, what I am asserting is that the really interesting physics of them may most likely dwell on a nonperturbative sector. QCD bound states (e.g. are there tetra-quarks?) is a similar example in QFT that equally can not be understood by any advanced kind of math available nowadays, except by computer methods and hard numerical processing: does it make it a “Not Even Wrong” theory? NO! Maybe It just proves that most brilliant humans are just stupid mathematicians when faced to Nature’s mysteries, but this also shows us that our specie is still very skilled in finding right answers by brute (numerical) force. BTW if IKKT is not a consesus around string theorists, BFSS model is, and you can see it is as (or more) suitable to numerical attack as QCD on deep infrared here: http://arxiv.org/abs/0707.4454
    You have a beautiful blog here, which is read by imminent physicists, maybe more of them will find it encouraging to try to find realistic nonperturbative ST/Matrix vacua, by aforementioned battle-tested methods from QFT, maybe dualities would be even part of the predictive game (e.g. in the spirit of hep-lat/0208020). Maybe even Matrix models will be for ST what Wilsonian latticization was for QFT.

    Merry Christmas


  8. CWJ says:

    Anon argues again trackbacks from arXiv to this blog .

    First, “Peter has a controversial and highly negative view of a significant fraction of current theoretical research.”

    Well, no. It’s controversial to string theorists. It’s not terribly controversial to physicists outside that subfield. Many will agree or disagree at some level, but it’s neither a radical nor a marginal position.

    Also, hello! string theory is not a “significant fraction of current theoretical research.” It’s a significant fraction of high energy theory. But that itself is only a small portion of theoretical physics. (If you look at NSF funding, it’s about 0.5% of all of physics, or maybe about 4-5% of all of theory; these numbers vary from year to year, of course.) It’s exactly this kind of egocentrism (theory = high energy theory) that Peter is arguing against.

    Second, Anon says ” many (though perhaps not all) scientists would be upset” to be linked to Peter’s criticism. My God, are you a physicist or a kindergarten teacher? Have you never received a referee report? Never been on a tenure committee? In a faculty meeting? Didn’t you have to defend a Ph.D thesis? Peter’s criticism is calm and measured compared to the vicious nastiness we face every day as working physicists. The idea that this blog will hurt the poor wittle feelings of those poor wittle posters on arXiv is raving nonsense.

  9. Chris Oakley says:


    Raphael Bousso appears to be a landscaper, and not the kind that can do something useful in your garden. Your blog enabled him to find another source of funding.

    You are therefore failing in your basic mission to stamp this kind of thing out.

    A careful re-evaluation may be called for.

  10. Lee Smolin says:

    Dear Joe and Peter,

    I agree with Joe that global symmetries cannot be fundamental and have made this point in both recent books. The reason is that global symmetries are forbidden in a relational framework such as general relativity. The principle that all observables represent dynamically evolving relationships implies that any two physically distinct events must be distinguishable by their values of local observables. Hence no exact global symmetries.

    This goes back to Leibniz’s principle of the identity of the indiscernible. Indeed, general relativity with spatially compact boundary conditions has no global symmetries, ie GR has no killing fields on its configuration space, as was proven by Kuchar in the 1970s.

    Symmetries feature in theories that describe subsystems of the universe and represent transformations of an external frame of reference relative to the subsystem modeled. Thus GR with externally imposed boundary conditions can have global symmetries which represent translations of their asymptotic regions relative to an isolated system. This is btw why a framework with asymptotic regions such as AdS cannot be a fundamental description of a physical theory.

    Penrose used to make a similar argument, and proposed long ago that all the global discrete symmetries, including time reversal symmetry symmetry and parity, should break down in a fundamental theory.

    This does not apply to gauge invariances, which reflect the presence of relational observables. Nonetheless, for other reasons I also agree with Joe that many fingered time may be emergent. It is indeed dual to a three dimensional local conformal gauge invariance, as is shown by shape dynamics.

    Best wishes for the holidays,


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