Quick Links

  • The LHC is getting close to the point where it can be restarted with a 6.5 TeV beam energy. Latest news here, schedule here. Plan is for a sector test late next week (beam in part of the machine), beam in the whole machine March 23. First physics run May 18th.
  • Next week there will be a conference in Venice devoted to neutrinos, blogging going on here.
  • There may be some progress on the Mochizuki/abc front. Ivan Fesenko has written up some notes that try and put Mochizuki’s ideas in context with some other more conventional parts of mathematics. The week after next will see a workshop in Kyoto, with lectures from Go Yamashita on the abc proof. Another recent survey talk by Mochizuki is here.
  • The latest AMS Notices has a series of articles about the life and work of Arthur Wightman, one of the main figures in the effort to make rigorous sense of quantum field theory.
  • In my essay about math and physics, I mentioned the Atiyah-Bott work on the moduli space of solutions to the Yang-Mills equation in the case of Riemann surfaces. This has an intriguing analog to the function field case, which was discussed already by Atiyah and Bott. Dennis Gaitsgory has a new paper out that touches on this in the context of his proof (with Jacob Lurie) of the Weil Tamagawa number 1 conjecture for function fields (see here). The new paper has the footnote: “The contents of this paper are joint work with J. Lurie, who chose not to sign it as author.”
  • Returning to physics, Princeton University Press announced that Frank Wilczek will edit a Princeton Companion to Physics, modeled on the wonderful Princeton Companion to Mathematics, which was edited by Tim Gowers. Publication is planned for 2018.
  • Caltech hosted a workshop the past couple days, inaugurating the Walter Burke Institute for Theoretical Physics. Hopefully they’re well-funded enough to put videos or slides online. John Preskill’s remarks at a celebration of the event are available here. He gives some principles for doing science that I very much agree with. In recent years I’ve become especially aware of the importance of his first principle: “We learn by teaching”, since I’ve been learning a lot that way. As the trend grows towards institutes modeled on the IAS and prestigious positions that involve no teaching, I think this needs to be kept in mind.

    I also agree with his last principle: “Nature is subtle”, and found very interesting his comments on the holographic principle:

    Perhaps there is no greater illustration of Nature’s subtlety than what we call the holographic principle. This principle says that, in a sense, all the information that is stored in this room, or any room, is really encoded entirely and with perfect accuracy on the boundary of the room, on its walls, ceiling and floor. Things just don’t seem that way, and if we underestimate the subtlety of Nature we’ll conclude that it can’t possibly be true. But unless our current ideas about the quantum theory of gravity are on the wrong track, it really is true. It’s just that the holographic encoding of information on the boundary of the room is extremely complex and we don’t really understand in detail how to decode it. At least not yet.

    This holographic principle, arguably the deepest idea about physics to emerge in my lifetime, is still mysterious. How can we make progress toward understanding it well enough to explain it to freshmen?

    From what I can tell, the problem is not that it can’t be explained to freshmen, but that it can’t be explained precisely to anyone, since it is very poorly understood. The AdS/CFT conjecture is now older than some of my current students, with a literature of more than 10,000 papers, but taking a look recently (see here) at what should be a toy model case (AdS3/CFT2) reminded me just how little seems to be truly understood. This is a quite odd and I think historically unprecedented situation.

  • Somewhat related to the holography question, for anyone interested in condensed matter physics, I recommend taking a look at Ross McKenzie’s blog Condensed Concepts. He discusses some of the issues related to attempts to use holography in condensed matter. He also has a recent paper (with Nandan Pakhira) showing a violation of a bound suggested by holographic arguments.

Update: On the multiverse mania front, tomorrow Science Friday is hosting Sean Carroll to continue his war against falsifiability and the conventional understanding of science, joined by Seth Lloyd to help promote the multiverse. Perhaps it should be “Pseudo-science Friday”?

Update: Michael Harris’s book now has a blog, which promises to discuss topics that didn’t make it into the book.

Update (March 7)
: Beam is back in the LHC (well, at least in a part of it). There was a successful test today, sending beam into one sector in one direction, two in the other, see here.

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41 Responses to Quick Links

  1. gadfly says:

    I’m very empirically driven and not an expert at all on quantum gravity, can anybody summarize or point me to a good summary of why the holographic principle, in spite of having no apparent empirical justification, is held in such high regard?

    This is not intended to be hostile in any way, I’m just genuinely curious.

  2. Peter Woit says:

    I think there are two main sources of physical interest in this, since it (adS/CFT) seems to non-trivially relate two different quantum theories:

    1. strong coupling on one side gets related to weak coupling on the other. So, for systems where you don’t understand the strong coupling theory (for instance string theory on the adS side, QCD or some condensed matter system on the CFT side), this promises to turn your problem into a weakly coupled one you can understand (e.g. a gauge theory on the CFT side, a weakly coupled gravity theory on the adS side). If this really works, it becomes a powerful calculational method for theories we otherwise know little about.

    2. Gravity theories on the adS side get related to more conventional field theories on the CFT side. This promises to make sense of quantum gravity.

    You’ll need an expert to explain exactly what the state is of understanding about when this works and how this works exactly (i.e. what exactly are the two dual theories, and what exactly is the mapping between them). One problem for the non-experts is to sort out what’s hype and what’s a solid result (I’m guessing Preskill’s “all information in the room is in the walls” business isn’t on the “solid result” side….). My recently quick attempts to understand what was known in the AdS3/CFT2 case didn’t get me far, which surprised me since we know a lot in that case about both sides of the correspondence (2d CFTs, 3d gravity theory).

  3. Ben R says:

    The idea of gravitational holography originally came from the Bekenstein entropy bound, which is convincing because it doesn’t depend on any particular theory of quantum gravity but only on the same sort of quasiclassical argument that gave us Hawking radiation. Take a look at gr-qc/9310026 and hep-th/9409089 (which predate AdS/CFT). The latter even has pictures showing how the projection onto the boundary is supposed to work.

  4. Art Brown says:

    Re “We learn by teaching”, it’s notable that the three examples Dr. Preskill referenced, Einstein, Schockley, and Bardeen, did not. Teach, that is. RIP, Bell Labs.

  5. Art Brown: Well, Bardeen did at UIUC after Bell Labs, but your point is taken.

  6. RogerP says:

    “From what I can tell, the problem is not that it can’t be explained to freshmen, but that it can’t be explained precisely to anyone, since it is very poorly understood.”

    “What can be said at all can be said clearly.” – Ludwig Wittgenstein –

  7. Alex says:

    On the topic of the holographic principle being held in such high regard, I have a naive question. What is the difference between the holographic principle and specifying the physics via boundary conditions? “all information in the room is in the walls” seems like an obvious quote given that the fundamental field equations are second order and hence are uniquely specified by giving the values of the fields on the boundary of the region?

  8. Peter Woit says:

    These are quantum field theories, not classical field theories. And, again, the real interest here is in the fact that strong coupling in the bulk theory is getting related to weak coupling in the boundary theory, and vice versa, allowing access to information about strongly coupled theories.

  9. Alex says:


    I acknowledge that relating strongly coupled theories to weakly coupled ones definitely seems like a result but now I’m confused by your statement: “These are quantum field theories, not classical field theories”. Are you suggesting there’s some sort of fundamental difference between solving a quantum field theory by specifying boundary conditions as opposed to an analogous classical field theory?

  10. Peter Woit says:

    Yes, the whole question of boundary conditions is very different in QFT, and the AdS/CFT story does not seem to be the conventional one about specifying boundary conditions. But I’d love to hear from someone expert who could tell us more about exactly what AdS/CFT does say (or at least provide references).

  11. gadfly says:


    Thanks, that was informative. I’ve only heard bad results about actual applications (for instance, I heard that AdS/CFT or something closely related can be used to get a theory of quark gluon plasmas, but with the fine print being that it is the worst such theory), have there been any cases where it has been exploited with undeniable success?

  12. Bernhard says:

    I read Sean Carrol’s piece again. Nothing I haven’t read before but still deeply disturbing. I suppose one should just ignore this sort of thing. It could be laughable it it weren’t so sad:

    “The truth is the opposite. Whether or not we can observe them directly, the entities involved in these theories are either real or they are not. Refusing to contemplate their possible existence on the grounds of some a-priori principle, even though they might play a crucial role in how the world works, is as non-scientific as it gets.”

    Is someone really refusing “to contemplate the possible existence” of a multiverse (who?) or is and others selling this as a serious scientific idea that deserves acceptance (and applause) based on nothing? He is completely misleading people here so to appear that people are being stubborn and blind to this great revolution whereas he and other geniuses are being so open minded. It reminds me that Feynman once said: “with an open mind I do not mean an empty mind!”

  13. Peter Woit says:

    I’m really the wrong person to answer that question. From what I’ve seen, the most detailed understanding is available in the case of AdS5/CFT4, relating N=4 SUSY Yang-Mills to supergravity and superstring theory. The interest there is that weakly coupled strings and gravity, which you can compute with, tell you about strongly coupled SUSY Yang-Mills. The applications to the quark gluon plasma involve making this work for the non-SUSY case, and it is there that I think the trouble arises and you no longer have a controlled approximation method.

    Sean keeps attacking the straw man who “refuses to contemplate” the multiverse, not acknowledging that serious multiverse critics do contemplate it, just don’t see any conventional scientific evidence for it, or any plausible path to getting any. If there’s no way to get such conventional scientific evidence, then contemplating the multiverse is much like contemplating the existence of angels and supreme beings. Nothing wrong with that, but it’s just not science.

  14. Anonyrat says:

    ” The AdS/CFT conjecture is now older than some of my current students….This is a quite odd and I think historically unprecedented situation.”

    The closest recent thing I can think of is renormalization theory – from Steukelberg (1943), Schwinger, Feynman (1948-49) – to Wilson (1971) — 28 years, enough interval for the birth to PhD of a physicist.

    There is a big difference with AdS/CFT, of course, that even when ill-understood, renormalization theory was known to work in the physical world.

  15. gadfly says:

    Why is Sean Carroll so committed to the multiverse?

  16. Peter Woit says:

    He long ago wrote a paper about how the multiverse would explain the arrow of time problem, and that had a lot to do with his first book. I have no idea how he got into that, it was at a time that the multiverse started to be a hot topic among string theorists.

    It has always mystified me why he’s running simultaneous campaigns for the multiverse and against religion. I would have thought that if you were intensely devoted to upholding science and rationality against religion, you’d be inclined to stay away from the parts of science that, at best, skate on the edge of what is science.

  17. student says:

    The introduction of arXiv:0912.0959 provides a fairly concise introduction to basic aspects of the AdS_3/CFT_2 correspondence and references to earlier reviews. Holography in this case is the correspondence between type IIB string theory on AdS_3 x S^3 x M and the CFT with target space Sym^N M where M = K3 or T^4 and N is taken to be large. Early checks of the duality included comparisons of the moduli spaces, (BPS/protected) spectra, and symmetries. More recent progress (circa 1999) is the matching of 3-point functions of BPS operators between the CFT and supergravity dual. The equality of the 3-point functions is explained by a very non-trivial non-renormalization theorem.
    One of the difficulties is that the dual string theory is not at the symmetric product orbifold point in the CFT moduli space. That is why many of the early checks compute quantities that are (covariantly) constant over the CFT moduli space. Going beyond protected quantities, the “toy model case (AdS3/CFT2)” is perhaps less developed than some of its higher dimensional cousins. For example the anomalous dimension of the non-BPS Konishi operator in N=4 SYM in the large N limit can be computed for all values of the t’Hooft coupling using spin chains and integrability.

  18. Jon says:


    I think there is a link between Sean Carroll’s commitment to the multiverse and his campaign against religion. The multiverse is often seen as a counter argument to the idea that the fine tuning of physical constants provide evidence for God.

    I’m pretty sure I’ve heard him use this argument in the past in debates against theists.

  19. Peter Woit says:

    What I’m wondering about is not the kind of very specific duality conjecture you mention, but the philosophy that this duality phenomenon is general, that (for instance) to every CFT2 you’ll get a gravity theory on AdS3. That’s what is being discussed in the Quanta article, or in Preskill’s claim about the boundary of a real room. What’s the exact conjecture there, what’s the evidence for it, and what’s the state of understanding of why it might be true?

    Also, how much recent progress is there? You refer to recent progress from 1999, but that’s now a very long time ago…

    Yes, but my point was more about his war against falsifiability, since that’s conventionally the first argument you make against the hypothesis of a deity (it’s unfalsifiable). The problem with “the multiverse did it” as an explanation of fine-tuning is again falsifiability. If you don’t have conventional scientific evidence for it, it’s the same sort of explanation as “the big guy upstairs did it”.

  20. Jim Harbough says:

    I read his blog (as well as many others). Sean loves Everett’s MWI and is almost fanatical about it. It strikes me that he is now focused on cosmological philosophical questions and less on being a physicist.

  21. Bernd says:

    The violation of the holographic duality bound is based on DMFT calculations, which is a bit like string theory for strongly correlated fermions in the sense that it is somtimes sold as “the only game in town”. Nobody knows how accurate these methods really are.

  22. Chris W. says:

    Both the multiverse adherents and the theists would have something if they could say that their favored explanation “explains fine-tuning [or whatever] in precisely this way [insert details here], and if you don’t believe me you can check it using these methods [insert details here].”

    Of course, they can’t do that. The theists don’t really care, because their agenda is apologetics for a faith, which is a nearly 2000-year-old practice originally directed at Roman overlords. The multiverse adherents have a somewhat different problem. They’re asserting that certain features of the observed universe are simply accidental, with no explanation in physical laws. The trouble is that they can’t point to actually existing alternative instances (of a universe) where those features differ or are missing. All they can do is conjecture that such instances exist, and then resort to the last refuge of scoundrels: “You can’t prove that they don’t exist!” The argument thus degenerates into another form of apologetics.

  23. Peter Woit says:

    What that paper is doing looks like the attempts to get “string theory” out of the strong coupling expansion in lattice gauge theory that were very popular when I was a grad student in the early 80s (work of people like Polyakov and Migdal). The problem with this is two-fold:

    1. You get some sum over a lattice version of surfaces, with certain weights, and you can call this “string theory” if you want, but it has no known relationship to what you normally call “string theory”, the continuum quantization of the vibrating string.

    2. To recover continuum gauge theory, which is asymptotically free, you want weakly coupled gauge fields at short distances. Here, you’ve got a strong coupling expansion, which is about not g=0, but g=infinity, with no way of getting to the physical g=0.

    Anyway, I haven’t read the whole paper, but I don’t see any new idea that gets around those old problems (or even any claim that what the author does gets around those problems). Unless I’m missing something the claim by the author to have the first explicit gauge-string duality is completely misleading, since this sort of relation between gauge theory and sums over surface has been well known since the late 70s, and is also well-known to not give you the kind of duality between gauge theory and a physical string theory that you are looking for.

  24. hopffiber says:

    >Also, how much recent progress is there? You refer to recent progress from 1999, but that’s now a very long time ago…

    I’m sure you know some of this, but every rational 2d CFT is proven to have a holographic dual theory of CS type, which can also be described as a topological string theory. This is thought of as a simpler sector of the full AdS3/CFT2 duality, where non-rational 2d CFTs are thought to be dual to (non-topological) string theories in AdS3. There is plenty of observations supporting this, but no real proof, but this understanding is for sure more recent than 1999.

    And of course there is continuously a lot of evidence for higher-dimensional specific cases of AdS/CFT produced all the time, through techniques like integrability, localization, entanglement entropy and so on. Of course the general case is very hard to study, so investigating “simple” examples is the best we can do. But the fact that a lot of examples do work in non-trivial ways do point to some degree of generality, at least to me.

  25. Mark says:

    Peter, here are two references that do what you want. They provide evidence that large-N CFTs with a gap in the spectrum of operator dimensions is dual to semiclassical gravity in AdS:

  26. Giotis says:

    Especially for AdS₃ I’m not sure I understand the point of the discussion.

    The fact that every consistent theory of QG in AdS₃ is a CFT₂ is ancient history. It was proven back in 1986 by Brown-Henneaux in the celebrated paper

    “Central Charges in the Canonical Realization of Asymptotical Symmetries: An Example from Three-Dimensional Gravity”.

    Specifically they showed that in AdS₃ the asymptotic symmetry is generated by a Virasoro algebra.

  27. Shantanu says:

    Peter and others to me, looking at the agenda of previous neutrino telescopes in venice workshops. experimental neutrino physics seems to be like experimental incarnation of string theory. Just as string theory makes no contact with experiment, experimental neutrino physics seem makes no contact with theory or any BSM physics, despite bold claims that it is first evidence for physics beyond standard model.

  28. Jeff M says:

    Pardon the ignorance of a mathematician, but I’m kind of curious about the whole AdS/CFT thing. I mean AdS has negative cosmological constant, and the universe has positive cosmological constant, no? So whatever the proposed duality is (and it is conjectured, not proved), what the hell does it have to do with the actual universe? Pretty, yes, if someone can actually prove it, but physics?

  29. Peter Woit says:

    Jeff M,
    There’s no claim that AdS/CFT itself has anything to say about the physical case of our universe. There is a hope that it might inspire finding a similar duality that would apply (see “dS/CFT duality”), but, like for many questions about generalizations of AdS/CFT, I’ve never understood exactly what the state is of the search for such a theory.

  30. bitboy says:

    Some thoughts on the arguments/comments by Sean Carroll and Seth Lloyd in the NPR segment:
    – Comments on falsifiability of string theory were disingenuous to say the least:
    – Contrary to what SC and SL stated, most folks that claim that string theory is not falsifiable don’t do so because the experiments are out of reach(Do they really think so many people that use the word “falsifiable” are so ignorant about such things?) but because there are _no_ real proposed experiments that can validate or invalidate string theory(“validate” in the sense of an experiment that can confirm some unique prediction of ST).
    – Sorry, “GR falls out of string theory” is not a valid argument.
    – They both seem to think that scientists should do science and leave philosophy to the philosophers and that physicists use “science should be falsifiable” as a catchphrase. Apparently these two physicists are the exception to this rule and are sophisticated enough in the philosophy of science to have the right to admonish other physicists in their use of philosophical ideas.
    – Sean Carroll states that “The lesson here is scientists should respect the field of the philosophy of science”. I guess they should do this by trashing certain parts of that field, like the idea of falsifiability. 🙂

  31. martibal says:

    Peter, a bit off topic but since you mention it and this is something I always wonder: is it possible in a few words to explain why there is no dS/CFT theory ? Is it just a technical difficulty, or there is a deep reason for which the A in AdS is important ?

  32. Peter Woit says:

    Maybe someone else has a good answer. My problem is that I don’t really understand why AdS/CFT, so no idea about why no dS/CFT. Many of the general arguments about the ubiquity of holography seem to apply to either dS or AdS.

  33. fg says:

    A rather intriguing statement I have heard about the AdS5/CFT4 correspondence is that the fifth dimension in AdS5 in a sense encodes the virtuality/off-shellness. In the CFT in 4 dimensions, there are loop corrections that correspond to the possibility of having virtual excitations (e.g. a quark that fluctuates momentarily into a quark+gluon state). In the AdS5 side of the correspondence, weak coupling corresponds to a purely classical theory that has no quantum fluctuations. The statement was that, for some specific observables, one can relate rather precisely the 5th coordinatein AdS5 to the virtuality of the modes that would be running in the loops in the QFT side of things.

  34. MathPhys says:

    On a different matter, I have just realized that Tullio Regge, one of the most original theoretical physicists in the 20th century, has passed away in October 2014. He was 83, and I don’t think that this was widely announced outside the Italian Physics community.

    His observation in 1957, at the age of 26, that scattering amplitudes in non-relativistic quantum mechanics are controlled by poles in the complex angular momentum plane led in 1967 to the Veneziano amplitude and from there to almost everything discussed in this blog.

  35. Peter Woit says:

    I’ve also heard it claimed that one could think of the 5th dimension in terms of the renormalization group flow. Again, I’ve never seen a precise statement.

  36. S says:


    I’m certainly no expert on AdS/CFT, but as I understand it, the geometric setting for the theory is an asymptotically hyperbolic manifold: take a compact manifold-with-boundary \bar{M} and put a metric g on the interior (M) such that g blows up to second-order. Then for any defining function f of the boundary (f is zero precisely on the boundary and df is nonvanishing there), f^2g is a metric on the whole manifold-with-boundary. We can choose different functions f, and so restricting f^2g to the boundary, we induce a conformal class of metrics there (but not a well-defined Riemannian metric). Hence the *conformal* in the CFT. The interior metric can then be expanded in a well-defined way in powers of the defining function, where the coefficients are determined by the conformal geometry of the boundary, say N.

    The problem is that the curvature of the interior metric is asymptotically -|df|^2, where this norm is taken in the metric f^2g. Thus, we can have negative-curvature metrics on the interior, or maybe asymptotically flat ones, but we can’t have positive-curvature ones.

    This I *think* is the reason, but I don’t claim to know a lot about Lorentzian geometry, or (goodness knows) the AdS/CFT conjecture.

  37. S says:

    (I should have noted that in order to have the above-mentioned expansion, the interior metric g must be Einstein — hardly a small point).

  38. My recollection is that the idea behind the connection with AdS and the RG picture is that AdS encodes the conformal group geometrically. I.e. the conformal group for the boundary theory is generated by SO(d+1,1) (for a Euclidean theory), and these appear as Killing vector fields which encode isometries of the AdS metric. Then it is natural to view the RG as a propagation through the space(time), say by following a one-parameter family of diffeomorphisms generated by the dilation operator, as you move away from the boundary theory. But I’m not sure if this is precisely how it works in practice, i.e. N = 4 SUSY Yang-Mills. In this (hand-waving) version it’s a very pretty idea that isn’t obviously tied to string theory.

  39. Sam says:


    Why does nobody say anything about the almost one year delay in the announcement of the Lucasian chair occupant? It is a rather curious situation for such a prestigious professorship.


  40. Bernd commented

    “The violation of the holographic duality bound is based on DMFT calculations, which is a bit like string theory for strongly correlated fermions in the sense that it is somtimes sold as “the only game in town”. Nobody knows how accurate these methods really are.”

    I disagree. My detailed response is here.

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