The Elephants in the Room – What every physicist should know about string theory

The string wars seem to still be going on, with the latest salvos coming from Ashtekar and Witten. In a very interesting recent interview, at the end Ashtekar has some comments about string theory and how it is being pursued. About claims that string theory is the only possible way to get quantum gravity he says:

I don’t know why science needs such statements; indeed, scientists should not make such statements. Let the evidence prove that it’s the only theory. Let the evidence prove that it is better than other theories or let its predictions be reproduced more than those of others. Science should not become theology. And, somehow such statements have a strong smell of theology, which I don’t like.

About AdS/CFT and the current state of its relation to quantum gravity:

We seem to be using these gravity ideas in other domains of physics rather than solving quantum gravity problems. I don’t think that the quantum gravity problems have been solved. And I have said this explicitly in conferences with panels – in which Joe Polchinski, Juan Maldacena and I were panellists – that, in my view, this is very powerful and these are good things. However, the AdS/CFT conjecture is the only definition of non-perturbative string theory one has – and it’s a definition, it’s not a proof of anything. It talks about duality, but there’s no proof of duality. To have a duality, A should be well defined, B should be well defined and then you say that A is dual to B. Since we don’t have another definition of string theory, we cannot hope to prove that string theory is dual to its conformal field theory. You can define string theory to be the conformal field theory. You have to construct a dictionary relating string theory in the bulk and conformal field theory on the boundary. That dictionary has not been constructed in complete detail.
Again, nobody is taking anything away from the successes that the AdS/CFT duality has had; but there is a big gap between the successes and the rhetoric. The rhetoric is at a much higher level than the successes. So, for example, in this conjecture, first of all the space-time is 10 dimensional. The physical space-time is supposed to be asymptotically anti-de Sitter, which has a negative cosmological constant. But we look around us, and we find a positive cosmological constant. Secondly, the internal dimensions in the conjecture, or this definition, are macroscopic. The Kaluza-Klein idea is that there are higher dimensions but because they are all wrapped up and microscopic, say, at Planck scale, we don’t see them. That’s plausible. But here, in AdS/CFT duality, they need the radius of the internal dimensions to be the same as the cosmological radius. If so, if I try to look up I should see these ten dimensions; I don’t. So, it can’t have much to do with the real world that we actually live in. These are elephants in the room which are not being addressed.
… there are these obvious issues and practitioners just pretend that they don’t exist. And that to me is unconscionable; I feel that that’s not good science. I don’t mean to say string theory is not good science, but publicizing it the way it’s done is not good science. I think one should say what it has done, rather than this hyperbole.

A good example of the problems Ashtekar is concerned about is provided by an article in the latest Physics Today by Witten with the title What Every Physicist Should Know about String theory. It’s devoted to a simple argument that string theory doesn’t have the UV problems of quantum field theory, one that I’ve seen made by Witten and others in talks and expository articles many times over the last 30 years. This latest version takes ignoring the elephants in the room to an extreme, saying absolutely nothing about the problems with the idea of getting physics this way, even going so far as to not mention the first and most obvious problem, that of the necessity of ten dimensions.

The title of the article is the most disturbing thing about it. Why should every physicist know a heuristic argument for a very speculative idea about unification and quantum gravity, without at the same time knowing what the problems with it are and why it hasn’t worked out? This seems to me to carry the “strong smell of theology” that Ashtekar notices in the way the subject is being pursued.

Witten is a great physicist and a very lucid expositor, and the technical story he explains in the article is a very interesting one, with the idea that most physicists might want to hear about it a reasonable one. But the problems with the story also need to be acknowledged and explained, otherwise the whole thing is highly misleading.
Besides the obvious problems of the ten dimensions, supersymmetry, compactifications, the string landscape, etc. that afflict attempts to connect this story to actual physics, there are a couple basic problems with the story itself. The first is that what Witten is explaining as a problematic framework to be generalized by string theory is not quantum field theory, but a first-quantized particle theory, with interactions put in by hand. This can be used to produce the perturbation series of a scalar field theory, but this is something very different than the SM quantum field theory, which has as fundamental objects fields, not particles, with interactions largely fixed by gauge symmetry, not put in by hand. For such QFTs, there is no necessary problem in the UV: QCD provides an example of such a theory with no ultraviolet problem at all, due to its property of asymptotic freedom.

Another huge elephant in the room ignored by Witten’s story motivating string theory as a natural two-dimensional generalization of one-dimensional theories is that the one-dimensional theories he discusses are known to be a bad starting point, for reasons that go far beyond UV problems. A much better starting point is provided by quantized gauge fields and spinor fields coupled to them, which have a very different fundamental structure than that of the terms of a perturbation series of a scalar field theory. A virtue of Witten’s story is that it makes very clear (while not mentioning it) what the problem is with this motivation for string theory. All one gets out of it is an analog of something that is the wrong thing in the simpler one-dimensional case. The fundamental issue since the earliest days of string theory has always been “what is non-perturbative string theory?”, meaning “what is the theory that has the same relation to strings that QFT has to Witten’s one-dimensional story?” After 30 years of intense effort, there is still no known answer to this question. Given the thirty years of heavily oversold publicity for string theory, it is this and the other elephants in the room that every physicist should know about.

Update: For another take on string theory that I meant to point out, there’s an article quoting Michael Turner:

Turner described string theory as an “empty vessel,” and added: “the great thing about an empty vessel is that we can put our hopes and dreams in it.”

The problem is that the empty vessel is of a rather specific shape, so only certain people’s hopes and dreams will fit…

Update: Many commenters have written in to point out this article, but I don’t think it has anything at all to do with the topic of this posting. There are lots of highly speculative ideas about quantum gravity out there, most of which I don’t have the time or interest to learn more about and discuss sensibly here.

Update: It is interesting to contrast the current Witten Physics Today article with a very similar one that appeared by him in the same publication nearly 20 years ago, entitled Reflections on the Fate of Spacetime. This makes almost the same argument as the new one, but does also explain one of the elephants in the room (lack of a non-perturbative string theory). It also includes an explanation of the T-duality idea that there is a “minimal length” in string, an explanation I was referring to in the comment section when describing what I don’t understand about his current argument.

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41 Responses to The Elephants in the Room – What every physicist should know about string theory

  1. manfred Requardt says:

    What Abhay Ashtekar is saying about String Theory and ADS/CFT is exactly to the point. I think it is a fair description of its scientific status.

  2. Warren says:

    You are being too positive.
    The real problem is that all approaches to high-energy theoretical physics are seriously flawed.
    The Standard Model is not asymptotically free.
    Even QCD is not saved by asymptotic freedom, which has the problem of renormalons.
    Experience with rigorous approaches, as constructive quantum field theory or lattice gauge theory, has shown us that nonperturbative approaches do not solve perturbative problems.
    Loop quantum gravity has problems even with the continuum limit, and doesn’t solve renormalizability of gravity, only regularizes it.
     
    But string field theory does exist, & people have addressed nonperturbative problems with it.
    So rather than denouncing or over-promoting the various alternatives, a more useful attitude would be to just admit that there is no well-defined approach to this problem yet, and recognize the practicality of complementary formulations that are all incomplete.

  3. martibal says:

    Is there a free link to Witten paper ?

  4. Bori says:

    Is this just an American phenomenon because of the culture of self-promotion and exaggeration resulting in a natural counter-reaction? Speaking to physicists in Europe, they seem to be more pragmatic about string theory – a certain proportion of positions goes to string theorists and they do their job, but no hype and no bad feelings.

  5. Tammie Lee Haynes says:

    Dera Dr Woit

    String Theory has “a smell of theology”?
    As a Christian, I am astonished that you would make such a statement.

    Christianity’s claims to being true are based on the accounts of witnesses to certain events such as the miracles of Jesus. The account of what a witness saw is the very definition of empirical evidence. (Of course, from time to time all of us find witness accounts to be non-credible, which is why you are not a Christian)
    But the point is this. Before String Theory can claim to have “a smell of theology”, it will need to have support from empirical evidence.

    Very truly yours
    Tammie Lee Haynes

  6. Charles Day says:

    Martibal, click again on the link to the article. You’ll find that it’s now free.

  7. anonymous says:

    “motivating string theory as a natural two-dimensional generalization of one-dimensional theories is that the one-dimensional theories he discusses are known to be a bad starting point”

    Loop quantum gravity itself has a roughly comparable foundational issue : we are assuming that the 3-metric tensor of gravity – or canonically transformed analogues – can be subject to a “quantization” procedure analogous to those developed for fields on Minkowski space-time treated as assemblies of harmonic oscillators : themselves quantized by techniques developed for non-relativistic finite degrees of freedom.

  8. Peter Woit says:

    Warren,
    I think there’s a difference between elephants in the room (we don’t know how to connect string theory to known 4d physics, with or without going to a string field theory) and something much smaller (mice? cockroaches?), such as the renormalon problems or the Landau pole at exponentially large energies.

    Charles,
    Thanks for making sure that Witten’s article is available.

    Tammie Lee Haynes,
    Perhaps theology is the wrong word. Maybe a better one for some string theory promotional activities would be “evangelical”, dedicated to spreading the good word. But, all, please resist temptation to discuss religion here.

    Bori,
    I don’t think there’s that much difference between string theorists in the US and Europe. There is a bigger market here for a small number that want to evangelize. However, one thing to say about both Ashtekar and Witten is that they are the sorts who would usually much prefer to stick to the technical details of the science, and not engage in public battles. I can see why Ashtekar might have had enough of the hype over AdS/CFT, I’m not so sure why Witten feels it necessary to make this well-worn claim at this point.

    Anonymous,
    Sure, a basic problem of quantum gravity is that we don’t know what fundamental variables to work with and/or what the correct quantization procedure is. Ashtekar is responsible (“Ashtekar variables”) for what seems to me the most intriguing such choice of variables.

  9. Tom says:

    There’s a new book coming out in December, published by CRC press, called “Why String Theory” by a young theoretical physicist named Joseph Conlon (found on Amazon). Though the description seems to indicated it is pro-string theory, does anyone have advance knowledge of its main premise? Just another semi-religious screed, or does it turn on any critical spotlights? (Admittedly, I wasn’t interested enough to do a thorough web search.)

  10. garcol euphrates says:

    A link from the interview in the Wire references one of Abhay Ashtekar’s formative books on cosmology, Gamow’s 1 2 3 … Infinity. The link referenced contains a reading list of science books (some of my favorites) compiled by a fellow named Robert Anton Wilson, a writer of some stature, who is quoted as:
    “Wilson also criticized scientific types with overly rigid belief systems, equating them with religious fundamentalists in their fanaticism.”

    Full circle!

  11. Peter Woit says:

    Tom,
    That book does look like mainly an advertising effort, an expansion of the web-site of the same name:
    http://whystringtheory.com/about/
    I notice there’s a chapter on “Direct Experimental Evidence for String Theory”. No page numbers, but I’m betting that one’s rather short…

  12. Dave Miller in Sacramento says:

    Peter,

    You wrote:
    >The first is that what Witten is explaining as a problematic framework to be generalized by string theory is not quantum field theory, but a first-quantized particle theory, with interactions put in by hand.

    This is something that has bothered me for decades, but that I rarely see discussed.

    Isn’t it the case that string theory does not even rise to the level of a non-relativistic first-quantized theory? It seems to me that it is the 2-D equivalent of Klein-Gordon, which, of course, does not give an acceptable version of probability (until you second-quantize it).

    Specifically, does free string theory , even in principle, actually give a probability for a string to have a probability (probability density function, of course) to actually be in a specific configuration in spacetime? If so, how you do numerically calculate this?

    Everyone: I am honestly not trying to score rhetorical points here against string theory. These are sincere questions, and if I am ignorant of work that answers these questions, please point to that work.

    Dave

  13. Dave Miller in Sacramento says:

    Warren,

    You wrote:
    >But string field theory does exist, & people have addressed nonperturbative problems with it.

    I have followed enough of your work to know that you have seriously worked on the subject: I truly appreciate that someone seems to take these issues seriously.

    Could you point us to the best source with the most concrete discussion of the existence of string field theory, if possible a source that addresses basic issues such as the state space, actual calculation of probabilities for at least the free string case, etc.?

    Thanks.

    Dave

  14. marten says:

    Does an empty vessel stop making most noise once filled only with hopes and dreams?

  15. Warren says:

    Peter:
     
    Renormalons are a low energy problem in QCD (strong coupling), not large, because of asymptotic freedom. They make QCD nonperturbatively nonrenormalizable. A related problem is nobody knows how to calculate parton distribution functions. In particular, nobody can do higher-twist corrections, because they require experimental input of more PDF’s, ad infinitum — more nonrenormalizability (in the sense of lack of predictability). Of course, you could calculate PDF’s if you could calculate confinement, but you can’t.
     
    Dave:
     
    Free string field theory is the same as string quantum mechanics, by the correspondence principle. Work has been done on nonperturbative vacua (due to the tachyon) for the bosonic string: The basic result is that the bosonic string is crap. So you need supersymmetry, but little has been done in SFT there yet. A similar situation exists in QFT in D=4, where you need supersymmetry to eliminate renormalons, by making the theory finite.

  16. Peter Orland says:

    Warren,

    QCD is far from a finished problem, but claiming renormalons ruin its properties is not an accurate statement.

    It is not known what the implications of renormalons are. They are special terms in perturbation theory, which (like instantons) ruin Borel resummability (all of which I’m sure you know). But there is no evidence that they render theories nonrenormalizable. There are models with perturbative renormalons which suffer from no such problem (I have worked on one of these). You may be familiar with the idea of resurgence, which does seem to deal well with Borel singularities in quantum mechanics (though not yet relativistic QFT).

    In any case, the lattice gives pretty good evidence that QCD is fine at large distance scales. There is even work under way to find pdf’s. The real problem is getting to extremely weak coupling (and string-inspired models do even worse).

    I am not disagreeing that there is a lot of work to be done in QFT (confinement, mass gaps, and a lot more), but it is not a failure.

  17. Warren says:

    Peter Orland:
     
    The only models I know of that solve the renormalon problem are quantum mechanical, not QFT. “Nonrenormalizability” comes from arbitrary coefficients of each ambiguity in the inverse Borel transform, corresponding to VeV’s of an ∞ # of composite color-singlet operators. This is quite analogous to higher-derivative terms in nonrenormalizable field theory (the higher-twist problem even more so). This problem is seen also in constructive quantum field theory, as well as an analysis by ‘t Hooft in the complex coupling constant plane. In lattice QCD, this shows up as nonuniversality @ the origin in coupling constant space.
     
    I did not mean to imply QCD was a failure. Only that it has problems, just as string theory does. But Peter Woit was implying that QFT was OK, in contrast to string theory being a complete failure. I would say string theory is the only theory that shows Regge behavior & spectrum of the type corresponding to confinement. Lattice QCD, on the other hand, has managed to calculate only ground state properties, & can’t deal with even rotational invariance, so can’t calculate cross sections.

  18. Bernhard says:

    ” A should be well defined, B should be well defined and then you say that A is dual to B. Since we don’t have another definition of string theory, we cannot hope to prove that string theory is dual to its conformal field theory.”

    I’m pretty sure I read this somewhere before…

  19. Peter Orland says:

    Warren,

    Whatever problems of consistency QFT has, there is no comparison to those of string theory. I’m not claiming this makes it better than strings, just that it is a much better-developed field.

    As to your first paragraph, one can do better than quantum mechanics. Asymptotically-free models in 1+1 dimensions have renormalon singularities in perturbation theory, yet there is good analytic evidence of sensible non-perturbative solutions. The exact S matrices are known, and there is even information about correlation functions.

    Concerning your second paragraph; there is no serious controversy whether lattice QCD (or any lattice QFT) will have rotational invariance, in the continuum limit, assuming that limit exists. Approximate rotation invariance is seen on the lattice, although a weaker coupling would be better. There is also some numerical evidence of Regge behavior (although this may not have been studied much in more than three dimensions). A lot more is known than ground state properties. I do not mean there are theorems or analytic solutions (yet), but the computer is a good guide to what the theory predicts.

    You are right to say that QFT has problems (which is why people work on it), but string theory is not as far along.

  20. ronab says:

    What are PDF’s? Googling the term just gets swamped by the other sort of PDF’s. Thanks.

  21. Peter Woit says:

    Warren,
    My comments were about UV problems, which is what Witten was writing about, and claiming that string theory solves, unlike QFT. I’m still quite surprised that Witten thought such a claim was what “every physicist should know about string theory”. I’d have expected that title to be used these days to make an argument for string theory as a way to handle strong-coupling problems, via its relation to AdS/CFT.

    From the talks of his I’ve seen, Witten likes to claim that in string perturbation theory the only problems are infrared problems, not UV problems. That’s never seemed completely convincing, since conformal invariance can swap UV and IR. My attempts to understand exactly what the situation is by asking experts have just left me thinking, “it’s complicated”.

    The problems with QCD are IR problems, and I’m certainly willing to believe they can best be addressed by finding some form of string theory dual to QCD. As far as I know, there’s no well-defined candidate for such a theory (i.e. that matches QCD in the UV, behaves like we think QCD should in the IR). QCD has the virtue that it works beautifully in the UV, and has a conjectural definition in the IR (via the lattice), even if it is hard to calculate things. I’m not claiming this is satisfactory, just that it’s completely inconsistent with the story Witten is trying to tell about string theory being necessary to solve QFT UV problems.

  22. Peter Woit says:

    ronab,

    PDFs = Parton distribution functions

  23. Warren says:

    Orland:
     
    I wasn’t disagreeing, only that string theory is by far better than alternatives to its problems. If you want to compare apples to oranges, pQCD is by far worse than QED. S-matrices in 2D massless theories isn’t much better, since only backward & forward scattering, so just numbers, not functions (& usually reduces to just 2->2). Proof of rotational invariance & being able to calculate anything with angles are 2 quite different things. Similar remarks apply to Regge behavior & getting an actual Regge trajectory. And properties vs. numbers, which you really get from lattice QCD basically for ground states.
     
    Woit:
     
    I hope you’re not confusing conformal invariance on the worldsheet with that in spacetime. As far as solving UV problems, I’m pretty sure Witten means in quantum gravity. String theory seems to solve that. No alternative does (although some people have a conjecture for 4D N=8 supergravity).

  24. andy norris says:

    “empty vessels make the loudest sound”

  25. Peter Woit says:

    Warren,

    The problem with Witten’s article is that his story about what goes wrong in QFT that doesn’t in string theory is about the small proper-time behavior of loops in perturbation theory, applying equally well to QCD and GR. Given the fact that QCD has no UV problem, it seems to me that the story he’s telling is likely irrelevant to the GR divergences problem.
    My earlier comment was about worldsheet conformal invariance, specifically the action of the modular group. Witten’s argument for no UV problem, for the torus case, is that the analog of proper-time in loop integrals takes values in the fundamental domain in the upper half plane, and this is bounded away from zero, so no small-time problem. There are lots of potential technical problems to worry about (you need this argument to work for arbitrary genus, in super-moduli space, etc), but what I was wondering about was the following: the modular group acts on this domain, taking it in particular to another domain that isn’t bounded away from zero. From another related angle, discussions of T-duality in string theory often claim that the right picture is that of some “minimum length”, below which you should go to a T-dual picture (acting by the modular group). But, if there are potential IR problems, how do I know that those IR problems in the T-dual picture don’t appear now as I go to the UV?
    To be clear, I believe there is likely some answer to this, cleanly separating out what’s UV and what’s IR, but it’s not there in the Physics Today piece as far as I can tell.

  26. Peter Orland says:

    Warren,

    “I wasn’t disagreeing, only that string theory is by far better than alternatives to its problems. ”

    I am not sure what you mean by this. It seems you are saying to say that string theory is on better theoretical footing than QFT. Such a position is simply not tenable. Calculations with QED and QCD aren’t perfect, but there are many reasons to trust them, not least of which is comparison with experiments. We agree that there are problems in calculating with QFT, but these do not invalidate its successes.

    And lattice measurements tell you more than vacuum properties (as I said earlier).

  27. Peter Orland says:

    I meant “trying to say”, not “saying to say.”

  28. Dave Miller in Sacramento says:

    Warren,

    You said:
    >Free string field theory is the same as string quantum mechanics, by the correspondence principle.

    Doesn’t string quantum mechanics suffer from the same sort of problem as “first-quantized” Klein-Gordon, i.e., no sensible meaning for probability? Can you suggest any place you can point me to where I can see how this works in detail?

    A possibly related problem that bothers me is how you actually get a concrete number for the “probability” (really the probability density) in first-quantized string theory given the use of the Gupta-Bleuler constraints. In QED, you can always drop Gupta-Bleuler and just go to the Coulomb gauge: You then are stuck with an apparently instantaneous Coulomb interaction, but at least probabilities more or less make sense (positive-definite Hilbert space inner product, etc.).

    Can you point me to any detailed discussion of how the analog of all this works in string theory? E.g., I am tempted to think there must be some analog of the instantaneous Coulomb interaction but have never seen this mentioned.

    Thanks.

    Dave

  29. Warren says:

    Woit:
     
    There are technical difficulties with higher-loop amplitudes in string theory, still being investigated. (A paper out today seems to claim to solve them.) But there are good arguments for finiteness that hold up to as many loops as have been evaluated. (Maybe they are proofs; I’m not enough of an expert to tell.) In any case, the arguments seem better then those for the next best alternative, 4D N=8 supergravity. (& for loop quantum gravity arguments indicate the opposite.) But you’re not going to get all the details into a Physics Today article.
     
    Orland:
     
    I meant to say that string theory is on more solid ground than any other quantum gravity theory, just as pQCD is for strongly interacting particles @ large transverse momenta. String theory clearly is not of as good standing as QCD, nor QCD as QED (“apples vs. oranges”). I am not aware of any calculations in lattice QCD that give the masses of radially excited hadrons as falling on linearly rising Regge trajectories, nor any that give low-energy scattering amplitudes of the sort described by nonlinear sigma models.
     
    Dave:
     
    @ the free level, strings are just a reducible, unitary representation of the Poincaré group. You can write the single-string Hilbert space as a direct sum of those for the “usual” particles. So if you understand free particles, you understand free strings. The free part of the string field theory action can be decomposed into the sum of field theory actions for particles of different spins. Nowadays quantization (for particles or strings) is better treated by BRST, which deals with unitarity in any gauge, particularly in the Feynman gauge, which is more practical than Coulomb gauge. Similar remarks apply to first-quantization: Stückelberg & Feynman solved the problem of the Klein paradox in that context by identifying “negative energy” particles as antiparticles. This interpretation can be applied either in classical mechanics, or in quantum mechanics in terms of the first-quantized path integral giving the Stückelberg-Feynman propagator.

  30. Warren says:

    Orland:
     
    P.S. By “ground states” I meant in the quantum mechanical sense (like the hydrogen atom), i.e., masses (& some couplings) of the π,ρ,N,Δ,…

  31. Peter Orland says:

    Warren,

    I think you are overly pessimistic.

    It’s true that most of the work on Regge trajectories in the lattice literature is only on glueballs, but there is no fundamental obstacle to asking the same question for mesons and baryons (it is more difficult, of course).

    There are attempts to work out scattering amplitudes. For example, the QCD corrections to light-by-light scattering are being studied on the lattice.

    I don’t work along these lines myself, but I don’t see them as impossible lines of inquiry.

  32. chris says:

    Warren,

    here is a recent review of excited lattice spectroscopy:
    arXiv:1411.0405
    And here is just one recent example of lattice calculations of scattering amplitudes:
    arXiv:1504.01717

    It is rather strange that you have singled out these two topics as unsolved by lattice, since there are major efforts going on in the US, Europe and Japan to address exactly these questions. There are of course things to be cleaned up (especially mapping out resonances in a finite box is a tricky thing) but there is no doubt whatsoever that the lattice will solve this in the coming years given enough computer power and algorithmic improvements.

    By the way, for us lattice people it is funny to see claims that “QCD is nonperturbatively nonrenormalizable” and such. You know, because of asymptotic freedom the continuum limit of the lattice regularization scheme is well defined and that is QCD. In N-flavor QCD you define the physical point by N+1 experimental measurments, you go there and out pop all other observables. We don’t care about perturbative approximations or models – if there are problems in them, they are not problems of QCD. QCD is perfectly well defined and consistent and we know how to do the path integral.

    Oh, and one more thing. Your claim
    “As far as solving UV problems, I’m pretty sure Witten means in quantum gravity. String theory seems to solve that. No alternative does (although some people have a conjecture for 4D N=8 supergravity).”
    is a rather gross misstatement. There is plenty of evidence that gravity is asymptotically safe and no UV problem exists to begin with. For a recent review, see e.g.
    arXiv:1202.2274

  33. TS says:

    Can someone explain to me what renormalization in a non-perturbative context means? Obviously, the meaning must be different than what we mean when we apply renormalization in perturbative calculations, namely the task of relating measured quantities to the quantities that appear in the calculation. Since the measured quantities involve all orders of perturbation theory, it is not trivial to see how the measured quantities can be related to the ones used in the calculation. In a non-perturbative setting OTOH I would expect that the objects entering the calculation are the ones we observe in the lab without any further requirements on the theory: say, two pions in -> machinery -> two pions out, where all pions have a mass of 140 MeV, spin 0 and charge = ±1 (and, except for the choice of units, these would come out of a sufficiently well-developed theory).

    A web search leaves me a bit puzzled: “non-perturbative renormalization” in this context appears to be not more than the setting of a numerical value for a mass (or several), which is more or less in line with what I would expect one needs for a non-perturbative computation, but why would one call this “renormalization” instead of “choice of units”?

  34. Peter Woit says:

    TS,
    This is starting to get a bit far afield from the topic of the posting. But I think the simple answer to your question is that whatever your definition of qft is, it appears to need a cutoff, and the cutoff qft will be characterized by certain parameters (“bare parameters”). You hope to compute observable numbers in terms of such bare parameters (in perturbation theory, by Feynman diagrams, non-perturbatively by some other method such as a lattice Monte-Carlo). The hope is to remove the cutoff, varying bare parameters with the cutoff in such a way as to get a well-defined limit for physical observables. This is what I’d call “renormalization” in general, perturbative or non-perturbative.

    A problem with Witten’s argument is that it’s purely about problems with renormalization in perturbation theory. If the short distance behavior of the theory is not governed by perturbation theory, such arguments will be irrelevant.

  35. Warren says:

    Chris:
     
    Thanks for the references; I’ll look them up. In fact, there is no proof that the continuum limit of QCD is universal, for the reasons I gave, & it’s exactly because of asymptotic freedom. By “nonrenormalizable”, I mean an infinite number of parameters must be introduced, because there are an infinite of renormalons, corresponding to an infinite number of color-singlet operators whose VEV’s must be determined. “The lattice will solve this in the coming years given enough computer power and algorithmic improvements” is something I’ve been hearing for 40 years; given Moore’s law you’d think it would’ve been done by now. So, yes, I have plenty of doubt. The only work I’ve seen on asymptotic safety in gravity is based on doing an ε epsilon from D=2, & I’m not satisfied by arguments that treat 2 as ≪ 1. In fact, any renormalization group arguments for finite changes in the coupling constant are dubious due to the arbitrariness of the β function past 2 loops.
     
    Orland:
     
    The only calculations I’ve seen on Regge trajectories in lattice gauge theories gives the result only near argument 0: the intercept & the slope @ 0. As to not seeing impossible lines of inquiry, I would say the same for string theory. Advances have been made in both in the last 40 years, both are hard problems, & both leave much to be desired.

  36. TS says:

    Thanks, Peter! The terminology makes a lot more sense to me now.

  37. Warren says:

    Chris:
     
    Looked @ 1 of your papers: Uses HAL QCD approach, which calculates a 2-body potential from the lattice, then plugs that into a (continuum) Schrödinger equation to find the results. Not sure how much advantage that has to the old quark model stuff that began with linear (for confinement) plus Coulomb terms. But I’ll keep reading…
     
    But the asymptotic safety reference is the same old thing. Hard to calculate in an ∞ dimensional coupling space.

  38. Attila says:

    While it is true that universality of the continuum limit in QCD has not been
    proven, if the continuum limit was not universal, I would not expect the
    continuum extrapolations of different observables, taken with different discretizations, to agree so well. Even if the low lying hadron spectrum and the equation of state at mu_B=0 was the only thing the lattice could calculate, which I think is not true, that would already be quite impressive, since no other method can do even that. I have to add that I am a lattice practicioner, so if I did not believe in lattice results in general, that would be somewhat strange.
    _
    “The problems with QCD are IR problems, and I’m certainly willing to believe they can best be addressed by finding some form of string theory dual to QCD.”
    I think that is optimistic. As far as I know, one does have dual theories to
    gauge theories closer to QCD than N=4 SYM, the problem is that the dual theory
    gets crazier as you get closer to the real thing, and the whole approach loses the
    computational advantage it had. An example of a computation in a theory closer
    to the real thing (N=2* SYM) is: hep-th/1108.2053

  39. Warren says:

    Attila:
     
    It’s all about optimism, isn’t it? People are optimistic about their own areas of research, & impressed with the results so far obtained, and dubious about claims in other areas. So lattice QCD can make good predictions for low energy (where renormalon contributions can be neglected, & plugging potentials into 1st-quantized calculations can be pretty good), with nothing but hopes for high energy, while the converse is true for string theory. Similar remarks apply to pQCD, which is good for large transverse momenta, where log corrections can be calculated, but power corrections (especially ones from higher twist) must be ignored.
     
    So we have a bunch of competing approaches staking out different “countries” in momentum space, each saying their country is better, & threatening to invade each other’s territory in the future. But history has taught us that these “threats” tend to be hollow, & people tend to ignore the diminishing returns from their own approaches. & each ignores the fact their own predictability problems prevent them from extending into the other territories, whether due to renormalons, twist, or compactification.

  40. Attila says:

    Warren:

    While I fundamentally agree, it seems I am more optimistic in general,
    and not only in the case of my own area. 🙂

    For example, in my own field (finite temperature field theory) there are
    actual examples where the applicability region of resummed perturbation
    theory and the lattice simulations overlap. In QCD (and even more in
    pure gauge theories) there are several observables, where high temperature
    lattice calculations can be compared to perturbative calculations, with
    good agreement. This includes the equation of state and fluctuations and
    correlations of conserved charges, for example.

    I do not think one approach needs to “rule them all”, it is not a realistic hope.
    A more realistic one would be to make contact, and find an overlap in the
    applicability of approaches.

    I know almost nothing about quantum gravity, but as an outsider, it does
    not seem completely hopeless to me that even if the UV completion is some
    kind of string theory, other approaches such as the asymptotic safety program
    with the functional renormalization group or CDT can be used as a low energy
    approximation of that. I could easilty be completely wrong on this one, but I
    don’t think I am wrong on QCD.

    Sorry for the off topic posts, I will stop now.

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