This evening a very interesting paper appeared on the arXiv, entitled Instantons Beyond Topological Theory I by E. Frenkel, Losev and Nekrasov. The authors are studying theories with a topological sector (supersymmetric quantum mechanics and 2d sigma models on a Kahler manifold, N=2 supersymmetric YM in 4d), but are interested in sectors of the theories that are not purely topological. I’m looking forward to reading the paper over the next few days, but it is a bit daunting. This paper is nearly 100 pages long, and it is only part I of three parts, and actually just the simplest part, that involving quantum mechanics.

HEPAP is meeting today and tomorrow, here’s the agenda. From the slides of the talk about NASA, the budget situation there for fundamental science missions doesn’t look good, and there is discussion of the upcoming NRC committee charged with figuring out which of the “Beyond Einstein” missions to allow to go forward. At Dynamics of Cats, Stein Sigurosson has been writing about this in terms of the missions being sent to Thunderdome, only one to emerge alive.

Slides from the talks last month at the conference in honor of Nigel Hitchin’s 60th birthday are available.

Joe Lykken has a nice review article about the standard model, in which he notes:

There is only one diagonal Yukawa coupling that is of order one, and that is the top quark Yukawa. But even this case is mysterious. The top Yukawa is not really of order one: it is equal to one! For example, using the 2005 combined Tevatron value for the pole mass of the top quark, the corresponding Yukawa coupling is 0.99 +/- 0.01. The entire particle physics community has chosen (so far) to regard this fact as a 1 per cent coincidence. I should point out that similar percent level equalities, e.g. supersymmetric gauge coupling unification or the ratio of the total mass-energy density of the universe to the critical density, have spawned huge theoretical frameworks bolstered by thousands of papers.

Difference is that, as far as I know, nobody has an idea why this Yukawa coupling should be one. Maybe this is a big clue…

Over at Backreaction, there’s an excellent posting about Does String Theory Explain Heavy Ion Physics?, one of the very few places to find a non-overhyped discussion of this topic.

Davide Castelvecchi has a well-done review of my book at his web-site.

At this week’s physics colloquium at Penn, Andre Brown reports that Robert Cahn emphasized that “half the particles needed for supersymmetry have already been discovered.” He also recalled a quote from another colloquium about supersymmetry: “Supersymmetry has stood the test of time. There is no evidence for supersymmetry.”

Update: A couple people have pointed out the following rather accurate cartoon.

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70 Responses to Links

  1. I think the coincidence of the top quark mass with the Yukawa coupling is not numerology, but a quite interesting observation – very few other “coincidences” of this kind exist, and Alejandro Rivero has noted a couple in recent papers.

    Should we shrug our shoulders at these coincidences ? I think we should take all clues we have from experimental data very seriously. However, there seems to be a sort of immobility in theoretical trends, and these clues do not get picked up with enough momentum… I Guess I know the reason.


  2. barbarian says:

    >Is anybody amused by the lack of sophistication of the
    >Standard Model circa 1996? What measurable quantities can
    >we calculate now that we couldn?t calculate then?

    I, for one, am. Let’s take 1994 instead of 1996, for the
    sake of argument.

    In 1994 we didn’t know whether the top quark actually
    existed, if it was standard, and what its mass was. We
    didn’t know that neutrinos have mass, that they oscillate,
    and whatever happened to the missing solar neutrinos. We
    believed that the cosmological constant was either small and
    negative or zero.

    In 1994 we thought that ST unambiguously predicted SUSY, and
    that the SSC was probably going to observe the MSSM.

    In 1994 most (if not all) of the 7 parton QCD amplitudes
    were not yet known. Unquenched lattice calculations were
    virtually unheard of. Two-loop computations in the SM were
    nowhere near as widespread as they are now.

    I’m just quoting from the top of my head. If I’d taken the
    trouble to actually checking the literature I’m certain I’d
    be able to write a much longer and precise list.

    A lot of progress happened in the last ten years. And a
    whole lot of stuff is going on right now. Lykken is
    definitely right.

  3. barbarian says:

    By the way, in 1996 nobody knew how to renormalize fully relativistic baryon chiral perturbation theory at the one-loop level…….

  4. Anon says:

    Bert wrote:

    “Thanks, and let me add that this subject is really not appropriate to be discussed in any weblog.”

    How many posts have you made on this weblog, about Rehren’s duality versus the Maldacena conjecture?

    Maybe you mean it is not appropriate to be discussed on any other weblog but this one.

  5. QWERTY says:





  6. woit says:


    I can’t honestly say that I’ve missed you and your defective keyboard, and in general I try and discourage off-topic comments. But I hadn’t heard about the Tao piece on the Poincare proof, which appears to be extremely good. The three available detailed proofs are hard to read, this looks like a much more accessible summary, an excellent contribution to the subject.

  7. nontrad says:

    re: our long lost cravings for QWERTY’s long lost defective keyboard…

    Too funny!!!

    Keep up the good work Peter: Such a healthy sense of humor is well worth it’s weight in gold.

    p.s. Don’t get me wrong, Tao is a large pile of papers in the corner of my office that I have yet to even begin to skim through. So good job QWERTY (even though it’s got nothing to do with nothing in this comment section).

  8. MathPhys says:


    Indeed, the central extension is not in Virasoro’s original paper. It was discovered by Joe Weiss right after Virasoro’s work became public.

    How come we don’t say “Virasoro-Weiss algebra”? Weiss died (he got himself killed on a weekend trek in the Juras while visiting CERN, or so I’ve been told).

    Anyway, these are historical comments of no scientific content.

    Re the discussion of Rehren’s work on Distler’s bolg: most illuminating (damn it Henning, you let the formalism confuse the issues, yet again). 

  9. Bert Schroer says:

    correct, as far as I remember Weiss died in an alpinist accident (similar to Renner who was Gell-Mann’s student).
    Besides the ST line there is also a field theoretic line via the c.r. of the energy-momentum tensor. In that case it is impossible to miss the correct structure, even for the case of free Fermions it is there. Follow the advice and do not confuse names of ideas with the protagonists of ideas. Strictly speaking the Born probability interpretation for the Schroedinger wave function appears the first time in Pauli’s work. But Max Born’s proposal to interpret the scattering amplitude in probabilistic terms of a cross section is morally the same as Pauli’s later contribution.

  10. MathPhys says:


    Thank you for the advice.

    Actually, Virasoro’s derivation (and presumably Weiss’ and everyone else’s after that) is precisely what you call “the field theoretic line”. It’s all 2-dimensional field theory. Virasoro was just careless.

    Historical quiz: When and where was Weiss’ central extension mentioned for the first time? In what context?

  11. Thomas Larsson says:

    Gelfand-Fuks 1968?

  12. MathPhys says:

    Is that so? Not Feigin-Fuks?

  13. Thomas Larsson says:

    There are many hits for Gelfand-Fuks cocycle, e.g. this. Among other things, I think Feigin and Fuks were the first to publish a proof that the Kac determinant is singular where it is, but that is a different story.

    John Baez has mentioned somebody who found the cocycle in characteristic p. Perhaps that was even earlier.

  14. Bert Schroer says:

    maybe some brief remarks concerning your doubt about the conformal decomposition theory (into conformal blocks) in my 1974/75 paper with Swieca and Voelkel could help you.
    I think you were expecting something similar to BPHZ (where the conformal block decomposition arose as an important tool for analyzing the minimal models) and you were disappointed. Since we did not have those models (only exponential Bose fields and the closely related massless Thirring model were at our disposal) we had to argue on purely structural grounds. Our decomposition theory was based on a prior observation called “the global causality paradox of CFT” which in turn originated from the observation that for certain zero mass fields with anomalous scale dimensions (e.g. the massless Thirring field) the Huygens principle was violated (the anticommutator was nonvanishing in the timelike region called the “reverberation” phenomenon). In such cases the global causality notion had to be adjusted to the covering of the compactified Minkowski spacetime (something which was already done before by Irvin Segal). The decomposition theory simply resulted from the realization that anomalous-dimensional conformal fields (in any even spacetime dimension), although behaving irreducibly under “small”conformal transformation, are highly reducible under the action of the center of the covering group; the resulting decomposition is the block decomposition theory. We also payed special attention to the 2-dim. situation for which one obtains a block decomposition for each chiral component. We were somewhat surprised about our findings because the component fields were not Wightman fields since they came with a source and a range projector. We did not continue our research (the minimal models could have been found by just pressing ahead, one does not really need to know anything about Kac-Moody algebras) because we thought that our rich decomposition theory had no genuinly nontrivial realizations.
    Let me tell you that I was impressed as anybody with BPHZ and it took me and Rehren almost 2 years to make the bridge from the old structural theorems to the new wealth of very nontrivial models (we published several joint papers on this subject).
    I have no problem with the way history developed. It is not only those who are too late who are punished by history (Gorbatchov); this is a fact of life.
    But it hurts me a bit if somebody claims that the old papers contain nothing. Deep ideas almost always have predecessors and the older results were usually obtained through very different arguments.

  15. MathPhys says:


    When you say BPHZ, I’m sure you mean BPZ as in conformal field theories, and not BPHZ as in momentum cut-off renormalization theory.

    Yes, I know of your earlier work (before BPZ) and I’m aware of the fact that you didn’t press ahead long enough.

    You know of course that others, most notably Gervais and Neveu were in a very similar situation. They also didn’t persist.

    I definitely have a lot of respect for your earlier works, and I didn’t mean at all to belittle it. I just wish to be very precise about what has been done before and after BPZ.

    I’m also familiar with your 2 papers with Rehren, and with Rehren’s paper on his own that followed your joint work.

    All the best.

  16. MathPhys says:

    PS So do you know where the first reference to Weiss’ central extension of Virasoro appeared in the physics (not mathematics)literature?

  17. Bert Schroer says:

    sorry, I meant BPZ. I do not know the work of Gervais and Neveu, is it published?
    The paper with Rehren on the exchange algebra of the conformal Ising model was the turning point when I really understood how the old stuff fitted together with BPZ. And it also increased my appreciation of Leo Kadanoff’s work (which in my opinion has been underestimated relativ to Wilson’s contributions).

  18. MathPhys says:

    Yes, Gervais, together with Neveu and/or others have an almost infinite series of papers, in which some aspects of BPZ were “anticipated”.

    Tell me if you, and no one around you, knows when and where was the first mention of the Virasoro central extension in a physics paper. Don’t be too proud 🙂

  19. Bert Schroer says:

    I think it was around 1972 for free Fermions via an explicit calculation by somebody around Dave Olive (Peter Goddard?). I am sure that I was not the first, but I may have been the first who derived it for the general case by an entirely structural argument. In any case my motivation was to find a class of “Lie fields” in the sense of Greenberg and Lowenstein; at that time my knowledge about string theory (the dual model) was closed to zero.
    Concerning Joe Weiss. I met him at CERN but I think his deadly accident did not occur in the Alps but after his return to the US in the Rocky Mountains. When you suggested that he may have seen the Virasoro algebra I agreed instinctively because he was extremely bright and certainly up to the task. But I do not know a reference. Alpine accidents were quite common within the particle physics community; besides bruno Renner I think that also heinz Pagels died under similar circumstances.

  20. MathPhys says:


    The first reference to Weiss’ result was in a footnote in a paper on strings by Fubini and collaborators (the Italian mafia at CERN). That’s when strings were a theory of hadrons in 4 dimensions.

    After using the Virasoro algebra without a central extension, the footnote reads

    “We have been informed by J Weiss that there is an extra term in the above equation. However, this does not change any of our conclusions”.

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