Not Even Wrong

I spent most of last week commuting down to Rutgers to participate in a workshop on “Groups and Algebras in M-theory”, organized by Lisa Carbone. Lisa was a student of Hyman Bass’s here at Columbia some years back, and in recent years has been working on Kac-Moody groups and algebras over finite fields.

Much is known about one special class of Kac-Moody algebras, the so-called affine Lie algebras. These are basically Lie algebras associated to loop groups, with a central extension. The study of the representation theory of these algebras is closely connected to quantum field theory in 2d space-time dimensions, and my first talk was about this topic. For more details about this, from the point of view I was taking, see the remarkable book by Pressley and Segal called “Loop Groups”, lecture notes from 1985 by Goddard and Olive at the Erice Summer School and Srni Winter school (see Int. J. Mod. Phys. A1:303, 1986), and Witten’s paper “Quantum Field Theory, Grassmanians and Algebraic Curves” in Communications in Mathematical Physics, 113 (1988) 529-600.

An elaboration of these ideas in one direction leads to the concept of a “Vertex Operator Algebra” (first introduced by Richard Borcherds), and the study of these was pioneered by Jim Lepowsky, who also participated in the workshop, together with his ex-student and now Rutgers faculty member Yi-Zhi Huang. Several other current and ex-students of Lepowsky and Huang were also there and gave talks. For more about vertex operator algebras, see the recent short review by Lepowsky, or the materials on Huang’s web-site. A VOA is essentially the same thing that Beilinson and Drinfeld call a chiral algebra, and these have applications in the geometric Langlands program.

What Lisa is really interested in is the non-affine case, where relatively little is known. Non-affine Kac-Moody algebras and groups seem to have no known tractable realizations, and many basic questions about both the algebras and the groups, as well as their representations, remain open. In recent years several of these algebras have been conjectured to have something to do with M-theory, most notably E₁₁, and the study of this connection has been the main focus of the work of Peter West, who gave a series of talks at the Rutgers workshop. For some more about this, see his recent papers, especially one on The Symmetry of M-theories. West’s graduate student P. P. Cook also has a weblog, and recently wrote a posting explaining a bit about this topic.

Greg Moore was at many of the talks and kept the speakers honest. He gave a fast-pace talk covering some older work, roughly the same material as in his paper with Jeff Harvey entitled Algebras, BPS States and Strings. I gave a second talk explaining a bit about my point of view on the Freed-Hopkins-Teleman theorem and its relation to representation theory and QFT.

After the talks Thursday afternoon there was a discussion section on what is going on with string theory, supersymmetry, and mathematics. No one was willing to defend work on the “Landscape” and I was surprised to find myself pretty much in agreement with quite a few people there about the way string theory has been pursued in recent years. On the whole the mathematicians are kind of bemused by the whole string theory controversy. The subject has certainly led to some very interesting and important mathematics, and they are happy to concentrate on that, although interested to hear about the controversy surrounding string theory in physics.

The Pacific Institute for Theoretical Physics, based at UBC in Vancouver, held a Showcase Conference a couple weeks ago, which was supposed to “celebrate the exciting new developments taking place in theoretical physics”. According to the organizers there are lots of exciting new developments in string theory, since six of the invited speakers (Myers, Ooguri, Randall, Schwarz, Shenker, Susskind) spoke on that topic, but no one at all spoke about elementary particle physics. There were also quite a few talks on condensed matter physics.

The talk of John Schwarz consisted mainly of the standard recounting of the history and basics of string theory that anyone who has been to conferences like this has heard a hundred times. This part stopped with Maldacena’s work more than 7 years ago. On more recent topics, about the anthropic explanation of the cosmological constant, Schwarz says: “Is there another explanation? I hope so.” He ends by putting up a long list of questions about string theory, more or less the same list everyone has had for twenty years now.

Steve Shenker spoke on Emergent Quantum Gravity, with “emergent” the new buzzword of the field. There was a separate workshop on emergence overlapping with the Showcase conference, organized by Phil Anderson and others, with Susskind the only string theorist allowed to speak there. Shenker introduced a new terminology to justify string theory: it is “An algorithmically complete, consistent description of quantum gravity”, although he does add the caveat “In certain simple situations (like flat space)”. By this I guess he is trying to get around the problem of how to claim that your theory is complete and consistent when you don’t know what it is. The idea is that at least you have an algorithm for doing computations. Perhaps he means perturbative string theory, although that is neither consistent nor complete (the expansion in the number of loops diverges). Perhaps he means a non-perturbative formulation like a matrix model, which works in 11 flat dimensions, but then he really should note that he’s not talking about quantum gravity in four dimensions, which is what most people care about.

There was an interesting panel discussion on The Theory of Everything?, which was moderated by Steve Shenker. He seemed mainly interested in making the obvious point that string theorists weren’t actually claiming that their theory explained anything about, say, biochemistry. The panel was actually balanced between string theory enthusiasts (Shenker, Schwarz, Randall), and skeptics (‘t Hooft, Unruh, Wald). Some of Shenker’s introductory remarks are inaudible, but he did repeat his claim about the “algorithmically complete” nature of string theory. “t Hooft had some quite interesting comments. He recalled that at a conference back in 1985 he had been the only one who didn’t think that twenty years later string theory would have solved all the problems of particle physics, noting that it was now 20 years later, he had been right, everyone else at the conference wrong. He was making the point that string theory now is extremely far from solving any problems in particle theory, and one can’t tell if this situation will change in 20, 200 or 2000 years. He tried to say some positive things about string theory, but they were pretty half-hearted. For instance he noted that dualities were very interesting, but they linked one ill-defined theory to another ill-defined theory. He also noted that in its present formulation string theory is only defined on-shell, which he takes as meaning that it doesn’t give a true local description of what is going on. He has reasons for being suspicious of people who claim that all one needs is an on-shell theory.

Schwarz attributed the TOE terminology to John Ellis. He said that he feels string theory is very far from explaining anything about elementary particle physics, that it was “almost hopeless to find the right vacuum”. He described what landscapeologists are doing in a skeptical tone, but didn’t actually criticize this. Answering ‘t Hooft, he claimed that back in 1985 he and Mike Green were actually more pessimistic than most other people about the prospects for getting quick results out of string theory.

Bill Unruh made the standard criticism that what is wrong with string theory is that string theorists are motivated by beautiful math, not physics. He doesn’t seem to have noticed that few string theorists are now doing math, since unfortunately most of them have taken to heart the criticisms of people like him. The failure of string theory has unfortunately reinforced the skepticism of many people like Unruh about the use of math in theoretical physics.

Wald quoted what sounded like a recent description of what string theorists think they are doing, then revealed that his quotes were from the 19th century, and referred not to string theory, but to the popular theory of the time that atoms were vortices in the ether. He deftly made the point that it is quite possible, if not likely, that string theory is just as wrong an idea as the vortex one.

Lisa Randall made some defensive comments about string theory as a guide for future research, even if it turns out not to work. These included the bizarre political analogy that it was wrong to worry about string theory ruining the credibility of physics, because, after all, the bogus WMD business didn’t seem to have hurt Bush’s credibility.

There were then some questions and comments from the audience. Susskind was in the first row, looking very peevish and defensive. He kept repeating that the field of theoretical physics had “no real choice but to track this down”, meaning to investigate the infinite landscape, and that this would take the efforts of many physicists. He explicity worried that funding agencies would not give any grants to anyone working on the landscape, to which Unruh responded that the shoe was really on the other foot, with some NSF panelists refusing to fund anyone who wasn’t doing string theory.

The conference web-site also includes an explanation of string theory which claims that in recent years string theory has “evolved very rapidly”, that the reason it can’t be tested is because of the small distance scales involved, and that it may be testable by observing a “5th force”, all of which is a load of nonsense.

Lubos Motl has an interesting post going over all the possible ideas he can think of that might lead to the next superstring revolution. Needless to say, they all sound extremely unpromising to me. Judge for yourself. He also quotes the promotional material for Susskind’s book due out late this year. It seems that “the Laws of Physics as we know them today are determined by the requirement that intelligent life is possible”.

Via Slashdot, an article that seems quite relevant to the current situation of string theory.

Earlier this week Jonathan Dorfan, the director of SLAC, announced a reorganization of the structure of the laboratory. The new structure involves four divisions, two scientific and two operational. One of the scientific divisions will bring together particle physics and astrophysics. It will be led by Persis Drell who also will be a deputy director of the laboratory, a position previously held by her father, particle theorist Sidney Drell. The other scientific division will be called “Photon Science”, which will make use of the SLAC x-ray sources. At the moment SLAC produces intense x-ray beams at the SSRL, using synchrotron radiation from a ring which is a descendent of the original SPEAR electron-positron ring that was crucial in the “November Revolution” of 1974 (and which also provided me with a job one summer).

The main SLAC linac is being turned into a free electron X-ray laser to be called the Linac Coherent Light Source (LCLS), which will be operational in 2009. At that time the plan is for SLAC to be out of the accelerator based high-energy physics business, with the PEP-II collider also shut down. The last fixed target experiment using the linac, E158, recently reported the most accurate measurement of the weak mixing angle at relatively low energies (at LEP it was very accurately measured at the Z pole). This measurement shows the running of the ratio of coupling constants predicted by the renormalization group. For more about this experiment, see an article in the latest Nature magazine.

This week’s Science magazine also has an article about particle physics. It reports on the HEPAP meeting mentioned here earlier where a plan to evaluate whether to shut down PEP-II or the Tevatron early was put forward. On a more positive note, the House Appropriations committee has restored some of the cuts in the FY 2006 DOE budget proposed by the White House. The House committe added $22 million to the high energy physics budget, bringing it back to the FY 2005 level (which, accounting for inflation, would still be a cut, but a smaller one).

An article in New Scientist about the same House bill explains that money is being taken away from the ITER international project to build a fusion reactor and used to bring funding for domestic fusion research also back to FY2005 levels. This may have something to do with the fact that the latest news about ITER is that a deal has been reached that will site it in France.

Last Wednesday night, a paper appeared on the arXiv that spelled very bad news for the whole “Landscape” scenario of how to get physics out of string theory. This paper produced what appears to be an infinite number of possible vacuum states for string theory, ruining hopes for getting predictions out of the Landscape by doing a statistical analysis of vacuum states.

Tonight a new paper by a prominent Landscapeologist (Michael Dine) has appeared. The abstract gives no hint of trouble, claiming evidence of “distinctive predictions for the structure of soft breakings”, but the beginning and the end of the paper tell a different story. The second paragraph of the paper admits that the infinite number of states destroys this research program, but deals with this by saying that the author will just ignore the problem for now:

“If this (infinite number of states) is true, many of the ideas discussed in this paper will have to be reconsidered…. the discussion of this paper will be predicated on the assumption that the number of relevant states in the landscape is finite and naive statistical ideas can be applied.”

In the paper’s conclusion, Dine states:

“There are many ways, as we have indicated, in which the ideas described here might fail. Perhaps the most dramatic is that the landscape may not exist, or alternatively that there might exist infinite numbers of states, whose existence might require signficant rethinking of our basic understanding of string theory and what it might have to do with nature.”

I’m looking forward to Dine and others finally getting around to “rethinking what string theory might have to do with nature”. It’s about time.

The US High Energy Physics Advisory Panel (HEPAP) is meeting in Washington yesterday and today, and some of the presentations are already available on-line. These include one from the DOE Office of High Energy Physics which notes that, given budgetary constraints, the only way significant funds will become available for new projects (including significant work on the proposed ILC linear collider), is by shutting down operations at the Tevatron or PEP-II. The Tevatron is now scheduled to operate until 2009 (at which point it can’t compete with the LHC), PEP-II at SLAC until 2008. The DOE is asking the P5 committee to advise about whether or not it might be a good idea to shut these facilities down early, and redirect the funds that are freed up elsewhere.

There are also reports on the status of PEP-II and the Tevatron. PEP-II and other accelerators at SLAC were shut down after an accident last October, only turned back on last month. The plan now is to run the machine steadily until July 2006, with only a one-month break in October. Presumably it’s down today, since if you try and connect to the SLAC web-site, you get a message saying that power is out at SLAC due to a tree falling and severing the main power feed to the site.

The Tevatron is doing well this year, recently achieving record luminosity, and its integrated luminosity so far this year is running ahead of even optimistic projections. It seems highly unlikely to me that the P5 committee will suggest shutting it down early.

There’s also a report from the ongoing National Academy of Sciences EPP2010 study of the future of US particle physics. Presentations from a meeting earlier this week at Fermilab are now available. These include presentations dealing with what is going on outside the US, including ones from DESY in Germany and KEK in Japan.

The biggest issue facing US particle physics is what to do about the International Linear Collider (ILC) project. In the presentation of Michael Witherell (ex-director of Fermilab), he notes that the world is in a transition from having five major labs running the largest accelerators to possibly only two: CERN with the LHC, and wherever the ILC is sited, if it is built. For US experimental high energy physics to remain a world leader, it is crucial that the ILC be built, and built in the US. Witherell recalls how the US HEP budget has declined by $100-150 million in real dollars over the last few years, but then gives a plan for the future that involves this budget increasing by 4% over inflation every year, something I find hard to believe is going to happen. The EPP2010 site also contains feedback they have received from various members of the community in response to questions about plans for the ILC.

In other experimental HEP news, the Experimental High Energy Physics Job Rumor Mill has been revived, joining the Theoretical Particle Physics Jobs Rumor Mill. Send them both your inside information!

Shamit Kachru (described by Lenny Susskind as the “master Rube Goldberg architect”) and collaborators have a new paper out this evening on flux compactifications, one that in a rational world should finish off the subject completely. Recall that Kachru is one of the K’s responsible for the KKLT construction of these flux compactifications that stabilize all moduli, and for the last couple years debate has raged over whether this sort of construction gives 10¹⁰⁰, 10⁵⁰⁰ or even 10¹⁰⁰⁰ possible string theory vacuum states.

Susskind, Arkani-Hamed, and other anthropic principle aficionados have argued that the fact that this number is at least 10¹⁰⁰ is a great triumph because it means that there are so many vacua that at least some will have small enough cosmological constant to be consistent with our existence. But if there are too many, all hope of getting predictions out of string theory disappears. With 10¹⁰⁰⁰ vacua, you can find not only the cosmological constant you want, but probably any values of anything particle experimentalists have ever measured or ever will measure, and the theory becomes completely unpredictive.

Even so, the study of these vacua has become more and more popular over the last year or two, with many arguing that, no matter how big the number is, at least it’s finite, so you have improved over the standard model, which has continuously tunable parameters. This argument was made in the panel discussion at the Perimeter Institute a month or so ago. Also, a finite number of vacua allows you to study their statistics, by assigning a weight one to each possible vacuum state and getting a probability measure by dividing by the total number. You can then engage in wishful thinking that this probability measure will be peaked about certain values, giving a sort of prediction.

The new paper gives a construction of flux compactifications of type IIA string theory, and in this case the authors find an infinite number of possibilities. This should kill off any hopes of extracting predictions from string theory by counting vacua and doing statistics. The authors try and put a brave face on what has happened, writing:

“we should emphasize that the divergence of the number of SUSY vacua may not be particularly disastrous. A mild cut on the acceptable volume of the extra dimensions will render the number of vacua finite.”

but then they go on to puncture their own argument by noting that:

“one can legitimately worry that the conclusions of any statistical argument will be dominated by the precise choice of the cut-off criterion, since the regulated distribution is dominated by vacua with volumes close to the cut-off.”

With this new result, the infinitesimally small remaining hope of getting predictions out of the string theory landscape framework has now vanished. It will be interesting to see if this slows down at all the ever-increasing number of string theorists working in this field.

Update: Lubos Motl has some comments about this same paper.

Someone wrote to me today to tell me that Harvard’s Nima Arkani-Hamed recently gave a lecture in Washington with the title “String Theory — Can We Test It?”. Somehow, I suspect that his lecture didn’t really give an honest answer to the question, since it would be hard to fill up an hour-long talk by just saying “No”.

Looking into this more carefully, it turns out that the talk was part of a “Dialogue on Science, Ethics and Religion” sponsored by the AAAS. At first I thought it was unusual to see a “Science and Religion” program paid for by anyone but the Templeton Foundation (for more about them, see here and here), but it turns out that they are the first organization listed in the list of those providing financial support for the program. I wouldn’t have guessed that the AAAS was in bed with Templeton and running programs on “Science and Religion”, but this kind of thing doesn’t surprise me anymore.

Arkani-Hamed’s talk was entitled: Naturalness versus the Superstring Landscape, or, Why Does The Universe Appear Finely Tuned? (not sure why it was advertised with the “String Theory — Can We Test It?” title). The organizer and “respondent” was James B. Miller, an ordained Presbyterian minister with a Ph. D. in Theology from Marquette University. From the abstract it appears that the talk involved Arkani-Hamed’s usual claims that split supersymmetry makes “sharp experimental predictions” for what the LHC will see (he seems to have a rather different notion of what an experimental prediction is than most scientists, much less what a “sharp” one is). He also seems to have implied that the superstring landscape scenario predicts split supersymmetry, something that actually isn’t the case, or at least is only true in the sense that the landscape predicts nothing at all, and thus is consistent with anything.

This past weekend I was in Cambridge and attended many of the talks at the JDG conference held at Harvard. The conference was nominally in honor of Shiing-Shen Chern, who died late last year, so many speakers made some connection between their work and Chern’s, especially his work on Chern classes.

Among the purely mathematical talks I attended was a very clear one by Victor Guillemin on Morse theory and convexity theorems on symplectic manifolds. The material he covered is quite beautiful, but rather old by now. His reason for covering it seemed to be that he has a new book on the topic (with Reyer Sjamaar) called “Convexity Properties of Hamiltonian Group Actions”, soon to appear from the AMS in the CRM monograph series, but also available on Sjamaar’s website.

Mike Hopkins gave an impressive talk on “Derived Schemes in Stable Homotopy Theory” which was based on very recent work by his student Jacob Lurie. This work involves defining a notion of a scheme which makes sense in the context not of the commutative rings of algebraic geometry, but instead the commutative rings of spectra in stable homotopy theory. It allows a new construction of the tmf (topological modular forms) theory of Miller and Hopkins.

Iz Singer reminisced about taking a class in geometry from Chern at Chicago in 1949, a class which he thought may have been the first one Chern taught in the US. Singer’s talk was about “Projective Dirac operators” which have an index which is a fraction. One of the main motivations for Singer’s original work with Atiyah on the Atiyah-Singer index theorem was to understand the integrality of the A-hat genus on a spin manifold as coming from the fact that it was an index. On a non-spin manifold the A-hat genus takes on fractional values, and one can use this to prove the non-existence of a spin structure. In work with Mathai and Melrose, pseudo-differential operator techniques are developed that allow one to define a sort of index in these situations where there is no spin (or even spin-c) structure.

There were several talks by physicists, or related to physics. One was by Kefeng Liu, half of which was about some new metrics on moduli space, the other half about some formulae coming out of work on topological strings. For this material, see his talk at last year’s Yamabe Conference. Vafa gave a talk on “Topological M-theory”, which he motivated by starting with the holomorphic anomaly in the topological string B-model. For quite a while it has been known that you can think of these topological string results as giving a vector in the Hilbert space one gets from quantizing H^3(M), where M is a Calabi-Yau. Topological M-theory is supposed to be something related to topological string theory in much the way the full M-theory is related to the full-string theory, so involves one-dimension higher. Thus it deals with 7-dimensional manifolds and tries to explain some of the phenomena related to topological strings on 6-d Calabi-Yaus in these terms. For more about this, there’s a talk by Andrew Neitze on-line that covers some of the same material.

Nikita Nekrasov’s talk was about “Z-theory”, which is his own name for the same ideas about topological M-theory that Vafa was talking about. He drew a version of the standard picture of the M-theory moduli space, now for Z-theory and with all sorts of mathematical objects attached to the various cusps. Nekrasov gave a similar talk in Nagoya late last year, as well as one at Strings 2004.

While a lot of interesting mathematics has come out of topological strings, the idea that that there is some grandiose unification involving thinking about 7d G2-manifolds seems to me even less promising than the idea of 11d M-theory itself, which for years now seems to have gone nowhere. Just as M-theory has led many physicists to pointless wanderings in 11-dimensions, it now seems to be leading mathematical physics away from rather rich mathematical areas into the complicated geometry of seven dimensions. Undoubtedly this will lead to some new mathematics, but it looks to me like it will be much less interesting than the mathematics emerging from string theory during earlier periods. The interaction between mathematics and physics remains dominated by the ideology of string/M-theory, and this is harming both subjects.

One aspect of the sad state of the interface between math and physics is that virtually no one from the physics department at Harvard seemed to be attending the JDG conference lectures. I’d been expecting to see at least Lubos Motl there, but he was down at Columbia attending a meeting on string cosmology. He reports on the talks here, here, and here, as usual covering very critically a talk on loop quantum gravity, quite uncritically one about the landscape and absurdly baroque constructions that try to make some contact with the standard model. I’m beginning to believe that his “leashing” did have something to do with his criticizing the landscape ideology too vigorously, since he seems to have stopped doing that.

For the latest on the landscape, see a recent talk by Lubos’s senior colleague Arkani-Hamed (whom he better not piss off too much) at the PHENO 05: World Year of Phenomenology symposium in Wisconsin, entitled The Landscape and the LHC. Arkani-Hamed’s talk begins with the usual strained historical analogy, this time a long and bizarre description of the calculation by Aristarchos of the distance to the sun by the method of parallax. The point of this is highly obscure, but seems to be that since Aristarchos was wrong to find unreasonable the huge distances to the stars implied by the lack of visible parallax, we’re wrong to find unreasonable the huge amounts of fine-tuning required by split supersymmetry.

He goes on much like Susskind for quite a while about the glories of the landscape idea, with the twist that supposedly split supersymmetry is “sharply predictive”. The only “sharp” predictions he mentions concern a relation between some coupling constants which haven’t been observed and likely never will, as well as that there may be a “long-lived” gluino. Not that he actually has a prediction for the mass or lifetime of this gluino.