Not Even Wrong

Nikita Nekrasov is giving a very interesting series of talks at the Jerusalem Winter School on the topic of “Introduction to modern covariant superstring theory.” The first of his talks was yesterday and is now on-line. In it he outlined the two main formalisms for superstring theory and discussed their advantages and drawbacks, while also giving a beautiful discussion of the quantization of the superparticle, and the use of twistor and pure-spinor methods in 10d super-Yang-Mills.

One of these two formalisms, the NSR formalism, uses supersymmetry on the world-sheet, with target space a usual (bosonic) space (i.e. 10d space-time). The advantage of this is that amplitudes are computed using a linear theory, supergravity on the worldsheet. One disadvantage of this is that spacetime supersymmetry is not manifest, only recovered after GSO projection. A very serious technical problem is that, while one ultimately wants to construct amplitudes by summing over spin structures and integrating over the moduli space, the formalism gives one for each spin structure an amplitude on the super-moduli space, not the moduli space (and these super-moduli spaces are different for different spin structures). In recent years D’Hoker and Phong have been able to deal with this problem for genus 2 (and they have some results for genus 3), but for higher genus how to consistently get amplitudes on moduli space remains an open problem. Note that the problem with these multi-loop amplitudes is not only that you aren’t sure they are finite, but you aren’t sure that they are even well-defined. Presumably this is purely a technical problem, not evidence of an inherent inconsistency problem with such amplitudes, but one can’t be sure of this until someone finds a way of resolving the problem.

The other formalism, the so-called Green-Schwarz formalism, uses a bosonic worldsheet, but takes the target space to be a supermanifold. This has the advantage of making space-time supersymmetry manifest, and avoiding the problem of integrating over super-moduli space, but it carries its own disadvantages. The world-sheet theory is now a highly non-linear, constrained theory, with both first-class and second-class constraints, constraints that Nekrasov describes as “hard to separate in a covariant way”. No one knows how to quantize this theory preserving super-Poincare invariance, so one typically uses a non-covariant gauge-fixing like light-cone gauge, something that runs into trouble at genus 2 or higher.

In recent years, Berkovits has been developing an improved version of the Green-Schwarz formalism, sometimes called the Berkovits formalism, and this is the main topic of Nekrasov’s lectures. Presumably Nekrasov will be discussing in his next two lectures how this works and some of the interesting problems with it, problems that he wrote a paper about a couple months ago, one which was discussed here. In his talk, Nekrasov seemed rather nervous that he would get into trouble because people might think he was raising the possibility of superstring perturbation theory being inconsistent. At one point he said that his “policy statement” was that he hoped that things could be made to work at any genus. He also seemed concerned in his talk yesterday about how his remarks might be reported today, saying:

There are really conc… well… I don’t want to call them conceptual problems because these days everything is recorded. If I say something is a conceptual problem, tomorrow there will be a blog on that, or a paper. So, there are some technical difficulties….

John Brockman’s Edge web-site has an annual feature where he asks a wide array of scientists and others how they would answer a hopefully thought-provoking question. Last year the question was What Do You Believe Is True Even Though You Cannot Prove It? This year it’s What Is Your Dangerous Idea?

There are responses to this question from 117 different people, a large fraction of them psychologists or cognitive scientists. Among the responses from physicists, several deal with the Landscape as a dangerous idea. Susskind takes credit for it, noting “I have been accused of advocating an extremely dangerous idea”, and that some of his colleagues believe it will lead to the end of science, leaving no way to defend physics as a truer path to knowledge than religion. He proudly describes the anthropic Landscape idea as “spreading like a cancer.”

On the opposite side of the issue, Brian Greene emphasizes the dangers of the Landscape philosophy:

When faced with seemingly inexplicable observations, researchers may invoke the framework of the multiverse prematurely — proclaiming some or other phenomenon to merely reflect conditions in our bubble universe — thereby failing to discover the deeper understanding that awaits us.

Paul Steinhardt is more emphatic about these dangers:

I think it leads inevitably to a depressing end to science. What is the point of exploring further the randomly chosen physical properties in our tiny corner of the multiverse if most of the multiverse is so different. I think it is far too early to be so desperate. This is a dangerous idea that I am simply unwilling to contemplate.

He also has his own “dangerous idea”, about a cyclic model of the universe explaining the small size of the cosmological constant. Lawrence Krauss gives his own version of an explanation of the danger that the Landscape will lead to an end-point for theoretical physics:

… all so-called fundamental theories that might describe nature would be purely “phenomenological”, that is, they would be derivable from observational phenomena, but would not reflect any underlying grand mathematical structure of the universe that would allow a basic understanding of why the universe is the way it is.

Some other interesting contributions from physicists come from Philip Anderson, who has some speculative comments about dark matter and dark energy, Lee Smolin, who discusses the possibility of natural selection having something to do with fundamental laws, and Carlo Rovelli, who remarks that we have still not completely absorbed the revolutionary ideas of 20th century physics:

I think that seen from 200 years in the future, the dangerous scientific idea that was around at the beginning of the 20th century, and that everybody was afraid to accept, will simply be that the world is completely different from our simple minded picture of it. As the physics of the 20th century had already shown.

What makes me smile is that even many of todays “audacious scientific speculations” about things like extra-dimensions, multi-universes, and the likely, are not only completely unsupported experimentally, but are even always formulated within world view that, at a close look, has not yet digested quantum mechanics and relativity!

The 23rd Jerusalem Winter School in Theoretical Physics started yesterday. The topic is “String Theory: Symmetries and Dynamics”, and it is organized by David Gross and Eliezer Rabinovici.

Some of the talks are already available on-line, with the quality of the video and audio very good, although you need the latest version of Apple’s Quicktime player. In his opening talk, Gross mentioned the recent New Scientist article quoting him as admitting string theory was in trouble, saying that the article misrepresented what he said. At the recent Solvay conference he had said something like “In string theory we don’t know what we are talking about”, and the New Scientist reporter interpreted that as meaning there was trouble, an interpretation Gross disagreed with. He was annoyed by the New Scientist editorial about the sorry state of string theory, and says he has been offered the opportunity to write a rebuttal and may do so. Gross went on to claim that really string theory is a vital subject and that it is in a wonderful period. He didn’t mention the Landscape.

Update: Another recent particle theory conference was the Christmas Meeting at Durham. There’s a report from the conference by blogger Paul Cook. Evidently Herman Verlinde is taking bets that string theory is the correct unified theory. Those who want to make some easy money might want to contact him. Then again, it’s unclear when you would get paid.

Update: The lectures by my Princeton classmate Igor Klebanov on using string theory to study strongly coupled gauge theories are particularly clear and interesting. Near the beginning he mentions this blog quoting it as saying “String theory is not good for anything.” I’d like to emphasize that that is not something I wrote or something that I think, I assume he is referring to one of my commenters.

Eckhard Meinrenken has been teaching a course at Toronto on Lie groups and Clifford algebras, and he has lecture notes available. This is beautiful mathematics and brings together several of my favorite mathematical topics: Clifford algebras, spinors, and representation theory of Lie groups. Some of this material is quite new, and very possibly has interesting applications in physics.

Dennis Gaitsgory, a new young tenured member of the Harvard math department, has been teaching a course on Geometric Representation Theory, and also has lecture notes available. These explain the “D-module” point of view on the subject.

My Columbia math department colleague D. H. Phong and fellow ex-Princeton grad student Eric D’ Hoker have a new paper on the arXiv called Complex Geometry and Supergeometry. It is based on Phong’s recent lecture at this year’s Current Developments in Mathematics conference at Harvard last month. D’ Hoker and Phong have been able to explicitly write down and show finiteness of superstring amplitudes at two loops, with the problem still remaining open at higher loops.

The arXiv web-site has a new look today. Gone are Paul Ginsparg’s “skull and cross-bones” icons like this.

Over the last month or so I’ve sent repeated requests to the arXiv to have trackbacks posted for several of my weblog postings. The first of these requests, back in early November, was answered positively by “mjf”, and the trackback (to a paper by Nekrasov) soon appeared. Since then I have sent repeated requests to the arXiv that they list trackbacks to my postings about papers by Weinberg, Baez, Freed-Hopkins-Teleman, and Tegmark et. al.. I’ve received no response whatsover to these requests, including to requests that they inform me of what the arXiv policy on trackbacks is and why my postings don’t seem to qualify.

Of the four postings involved, two of them (about the papers of Baez and Tegmark et. al.) led to discussions here involving some of the authors of the papers themselves, and I think seeing this discussion could be valuable to people interested in those two papers. I can think of no legitimate reason why trackbacks to those postings should not be allowed. The posting about Freed-Hopkins-Teleman was intended to point physicists to some very interesting new work in mathematics; I also believe some people might find that valuable. Finally, the posting about Weinberg’s article was perhaps more controversial, but I believe it raises legitimate issues that the particle theory community needs to allow public discussion of, and censorship of this is inappropriate.

I’ve looked a few times at the list of recent trackbacks to see if I can figure out from that what the arXiv policy about this is. Today’s list of trackbacks from the period December 20-23 has 6 listings, one from cs.unm.edu and five from golem.ph.utexas.edu. As far as I can tell, at least as far as particle theory is concerned, the arXiv trackback system is being run mainly for the benefit of the owner of golem.ph.utexas.edu, who sits on the arXiv advisory board, and may or may not have something to do with the censoring of trackbacks to my postings. Of course I have no way of actually knowing what is going on here or who is responsible. This situation seems to me to raise questions which the arXiv advisory board needs to address, and I am simultaneously contacting them about this.

Update: I still don’t know exactly what is going on at the arXiv, but from what I’ve heard so far, it is clear that the problem is not a technical or administrative one, so I’m removing the question mark that used to be there in the title of this posting.

Time now to ignore this for a while and start celebrating the holiday with family and friends. Happy holidays to all!

Update: Still no word from the arXiv. Commenter Jose notes that trackbacks to comments at physcomments.org do generally appear on the arXiv. There are instructions at physcomments.org that say:

If and only if a blog annotation starts with an identification paragraph “A Comment by …”, and its subject line starts with the preprint it is commenting about, then it is submited to the ArXiV for consideration. Note that currently the ArXiV reserves its right to reject the trackback ping.

Evidently Alejandro, who runs physcomments.org, has been successful in not only communicating with the arXiv, but getting them to post his trackbacks. He comments here that “It is only via Distler that it has been finally incorporated, and it is partial, experimental etc.” From this I take it that the key to getting arXiv trackbacks posted is, as commenter Chris Oakley suggests, to not have pissed off Jacques Distler, something I seem to have done long ago with my criticisms of string theory.

I’m more and more convinced that what is going on here is all due to the simple fact that Distler doesn’t like me. I was surprised and saddened to note that in his recent posting about Raoul Bott, he links to other postings about Bott by Sean Carroll (who credits my blog as where he learned of Bott’s death) and Lubos Motl, but not mine. I also didn’t realize that Distler was a couple years behind me at Dunster House, an experience that perhaps he has yet to get over.

Update: While I was writing the above, Alejandro submitted a comment noting that, after initial problems getting his trackbacks accepted “now it seems I am allowed to send trackbacks. Of course, one never knows when this permission can change again.”

This week’s issue of Nature has short articles by Atiyah and Witten, both addressing the issue of the current state of string theory.

Atiyah’s piece is an interesting review of Lawrence Krauss’s new book Hiding in the Mirror entitled Pulling the strings, and it concentrates on what Krauss has to say about the relation of mathematics and physics. Krauss ends his book quoting the mathematician Hermann Weyl as choosing beauty over truth, remarking that physicists don’t have this luxury. Atiyah points out the story of Weyl’s work on gauge theory, which Weyl published over Einstein’s strong argument that it was physically wrong. The idea was just so beautiful that Weyl felt there had to be something to it, an opinion that turned out to be amply justified as the concept of a gauge theory has turned out to be among the most fundamental ideas in theoretical physics.

Witten’s piece is entitled Unravelling string theory and it tells the story of how he got interested in string theory and offers a defense of its continued study despite the lack of progress during the past 21 years in using it to come up with a unified theory. His defense consists of three points:

1. It appears to be a consistent generalization of QFT, and is worth study on that grounds alone.

2. It incorporates general relativity and provides a “rough draft” of particle physics.

3. Research on string theory has led to all sorts of spin-offs: insights into confinement, black-holes, mathematics.

Those are certainly the strongest arguments for working on string theory, but I find it disappointing that Witten chooses to ignore much of what has been happening in string theory over the last few years. He addresses only by indirect allusion the whole issue of the landscape and the strong possibility that the string theory framework for unification is inherently incapable of predicting anything. Witten would do particle theory a huge favor by at least acknowledging that if the string theory landscape really exists, it is not, as many seem to think, a new paradigm for how to pursue theoretical physics, but instead the end of hopes for this idea about how to achieve unification.

Someone wrote in to tell me about a very interesting interview with Alain Connes, conducted at the IPM in Teheran at the time of the Workshop on Non-Commutative Geometry held there this past September.

As always, Connes has quite a few provocative things to say, including some harsh criticisms of the way string theory research is conducted (this in spite of the fact that the Institute hosting him is dominated by string theorists):

The only thing I resent in string theory is that they put in the mind of people that it is the only theory that can give the answer or they are very close to the answer. That I resent. For people who have enough background it is fine since they know all the problems that block the road like the cosmological constant, the supersymmetry breaking, etc., etc.. But if you take people who are beginners in physics programs and brainwash them from the very start it is really not fair. Young physicists should be completely free, but it is very hard with the actual system.

Connes also has many interesting comments about non-commutative geometry and about his own career, including the fact that he went off in the direction he did because he was put off by the arrogance of the algebraic geometers at the IHES. He also has a lot to say about the importance of having a system like the French CNRS system that allows talented young researchers to develop a long-term research program without too much pressure to achieve quick results. He is quite scornful about the US university system, which he sees as emphasizing money and subjecting young people to huge pressures to work in well-established areas instead of trying to do something new and ambitious.

The interview also contains quite a few amusing stories. In one of them Connes tells about a well-known string theorist who walked out of his talk at Chicago because he wasn’t very interested, but two years later was paying rapt attention to the same talk when Connes gave it at Oxford. When Connes asked him about this, the physicist told him that the difference was that in the meantime he had heard that Witten had been seen reading Connes’s book in the library at Princeton.

On a completely different topic, there’s a nice review article by Edward Frenkel on the Langlands program and conformal field theory. Witten has new ideas about this subject and how it is related to S-duality in four-dimensional gauge theory. I hear he has been working on a paper on the subject since this summer, and that it should appear imminently.

There’s an interview with Susskind in the latest issue of New Scientist by Amanda Gefter, entitled Is String Theory in Trouble? Susskind makes many of the same points as in his recent book The Cosmic Landscape: mixing up positivism and falsifiability, attacking those who ask for falsifiable predictions as “Popperazi”, and saying that the best he can come up with as a prediction from his ideas is the very long-shot that the negative curvature of space due to its origin in bubble nucleation has not been made vanishingly small by inflation.

There’s a discussion forum about the article on the New Scientist site that people might want to contribute to.

Update: Ken Silber writes in to point out that William Dembski, one of the most prominent Intelligent Design ideologues, has now latched on to the string theory controversy as evidence that mainstream science is no better than ID. Dembski has both comments on Susskind and comments on David Gross’s admission that string theory is in trouble.

I’ve been pointing out to string theory partisans for a while that they need to publicly confront Susskind and his followers over their abandonment of the scientific method, otherwise they will have no argument against Intelligent Design. Susskind is making all this much worse with his dismissive comments about the falsifiability of evolutionary theory, as well as the following from the New Scientist interview:

If, for some unforeseen reason, the landscape turns out to be inconsistent – maybe for mathematical reasons, or because it disagrees with observation – I am pretty sure that physicists will go on searching for natural explanations of the world. But I have to say that if that happens, as things stand now we will be in a very awkward position. Without any explanation of nature’s fine-tunings we will be hard pressed to answer the ID critics. One might argue that the hope that a mathematically unique solution will emerge is as faith-based as ID.

Update: Susskind is fast becoming the darling of the IDers. A new posting on the web-site “Intelligent Design the Future” run by the Discovery Institute links to a review by IDer and nuclear physicist David Heddle entitled Susskind’s Sophie’s Choice.

Heddle concludes:

Susskind has presented the physics community with what is, for some (not this writer), a Sophie’s Choice: a hidious, complictated, unfalsifiable String-Theory Landscape, or Intelligent Design.

Susskind rocks.

Various and assorted things that may be of interest:

Joshua Roebke at Seed has accumulated opinions about the landscape from various physicists. No real surprises; Witten wins the award for most non-committal:

I just don’t have anything incisive to say. I hope we will learn more.

There’s a mailing list called philphys devoted to “philosophical and foundational problems of modern physics.”

The web-site for the ICFA Seminar held in Korea a couple months ago has several interesting presentations on-line, including one by John Ellis, and several about future plans at various accelerator laboratories world-wide.

There was a conference recently in Geneva celebrating the 100th anniversary of the birth of E.C.G. Stueckelberg. Some anecdotes about Stueckelberg are here.

There is a bit of a controversy about another E.C.G., Sudarshan, who some (including himself) feel should have been part of this year’s Nobel prize in physics. Stories about this here, here, and here.

Some talks given at the recent conference at OSU on Strings and the Real World are on-line. See if you can find anything in them about the real world.

According to this article, string theory is now being marketed to the 6-11 year-old age group, appearing as test questions in the Flashcard Fishing game on the GoGo TV game system.

Barry Mazur has an article about category theory entitled When is one thing equal to some other thing?.

Penn State mathematician Adrian Ocneanu has designed a sculpture representing an interesting four dimensional figure, the Octacube.

Update: Sean Carroll has a new preprint out entitled Is Our Universe Natural?, and some commentary about it at Cosmic Variance. Unlike certain Nobel prize winners, Sean recognizes that before throwing in the trash the paradigm of how to do theoretical physics that has had such success for many centuries, one should at least have a shred of scientific evidence for one’s proposed alternative. He explains what the problems are with the one supposedly successful “prediction” of the anthropic principle, that of Weinberg for the cosmological constant, noting that it makes three assumptions, and :

The first of these is a guess, the second is likely to be fantastically wrong in the context of eternal inflation, and the last only makes sense if all of the other parameters are held fixed, which is not how we expect the multiverse to work.

Even with these dubious assumptions, the “prediction” one gets is off by more than an order of magnitude.