Not Even Wrong

Eric D’Hoker and D.H. Phong this past week finally posted two crucial papers with results from their work on two-loop superstring amplitudes. The first one shows gauge slice independence of the two-loop N-point function, the second shows that, for N less than 3 and for low-order terms at N less than 4, there are no two-loop corrections to the low energy effective action.

D’Hoker and Phong have been studying superstring amplitudes for nearly twenty years, and are justly proud of their recent results, which are a tour de force of careful calculation. Over the years there have been many claims made about two-loop amplitudes, but until their work, no one had managed to really sort out the gauge dependence issues and write down gauge-independent amplitudes. For some comments about some of the issues involved at genus 2 and higher, see postings by Jacques Distler here, here, and here.

I don’t think D’Hoker and Phong will be coming out with complete results for genus 3 anytime soon, so the state of the art is that there is now a finite and well-defined version of the two-loop superstring amplitudes, with the problem of higher loops still open. While claims abound about the finiteness of higher-loop amplitudes, before believing them one should first take a look at the tricky problems that D’Hoker and Phong had to overcome to get well-defined two-loop amplitudes.

Update: Jacques Distler has a new posting about multi-loop amplitudes and potential problems with the Berkovits version of the superstring (he explains in more detail the possible problems with the BRST and picture-changing operators I mentioned). For some mysterious reason Jacques neglects to refer to my posting or comments about this. I encourage those commenters who seemed convinced I didn’t know what I was talking about to now take up their arguments with him.

If you’ve been following the story of the “Landscape” over the past year or so you’d remember that its proponents felt that if it could predict anything it should be able to predict whether or not there will be supersymmetry at low energies. They had great hopes for making this prediction before 2008 when the LHC presumably will tell us whether there is supersymmetry at LHC energies.

Well, tonight one of the biggest proponents of this point of view, Michael Dine, has a new paper out with two co-authors, entitled Branches of the Landscape. In it they conclude:

“From all this, it appears that it is difficult, in principle, to decide whether or not the landscape predicts supersymmetry.”

So, many string theorists now seem to believe that:

1. String theory predicts a landscape of possible vacua.

2. Given the existence of such a landscape, one can’t predict whether or not there will be low-energy supersymmetry (or anything else either).

One wonders it these string theorists ever studied elementary logic and can draw the obvious conclusion from 1. and 2.

The transparencies from the conference on twistor string theory held two weeks ago at Oxford are now available on-line.

Quite a few of the talks deal with the technical details of computing amplitudes. For the motivation from phenomenological particle theory, see the talk by Zvi Bern. As for the motivation and present state of the whole idea of relating QCD to a string theory in twistor space, the only person who really seems to have much to say about this is Witten himself. His transparencies are in three parts: part 1a and part 1b from his first talk and then a second talk in which he explains what the problems with the whole idea are and some ideas he’s been thinking about using to try and get around them.

There’s a quite interesting article on the controversy over string theory that appeared yesterday in the Boston University student newspaper. It gives some insight into the political battle now going on in many physics departments.

The Boston University physics department has always been in the shadow of its more prominent neighbors just across the river in Cambridge. A few years ago they attracted Glashow away from Harvard, and I’ve been told a big selling point for him was that he would no longer have to be part of a department dominated by string theorists. He’s one of very few particle theorists who has consistently and publicly complained about what is going on in string theory. In the article, he forcefully makes the analogy between Einstein’s failed unification efforts and string theory:

“It is tragic,” Glashow said, “but now, we have the string theorists, thousands of them, that also dream of explaining all the features of nature. They just celebrated the 20th anniversary of superstring theory. So when one person spends 30 years, it’s a waste, but when thousands waste 20 years in modern day, they celebrate with champagne. I find that curious.”

Ken Lane, one of Glashow’s colleagues at BU, says that “String theory is not physics” and that he doesn’t know of any BU faculty who think that string theory belongs in the physics department. He does seem to think that it belongs in a math department, something I have some problems with. While certain parts of string theory are mathematically interesting and do belong in math departments, most of what string theorists do is not mathematics. For instance, the many string theorists making anthropic arguments about the “Landscape” are not doing mathematics and it’s pretty insulting to mathematicians to say that they belong in math departments.

Lane believes string theory is on its way out, and that the LHC will finish it off:

“I think I can safely predict that string theory is going to wither and die when exciting results start coming out of the LHC.”

Cumrun Vafa of Harvard seems to be spitting mad at the idea that BU won’t hire string theorists, referring to them as “foolish” and “childish”, which is not normally language academics use when talking to the press about their Nobel-prize winning colleagues at neighboring institutions. Vafa was a student of Witten’s a year or two behind me at Princeton, but I haven’t talked to him since my postdoc days. He’s definitely a smart guy, but also definitely a fanatic.

Vafa graduated from Princeton in 1985, just as the string theory fad hit. He went to Harvard as a postdoc, where most of the senior people were pretty skeptical about string theory, although willing to hire smart young postdocs doing it. I heard he was very upset in 1986 when Glashow published his article with Ginsparg in Physics Today attacking string theory, and even threatened to leave. But over the next decade or so he managed to marginalize Glashow, get more string theorists hired, and consolidate power around them. Finally Glashow left, and by now the string theorists heavily dominate the theory group. Of the active theory faculty, Vafa, Strominger, Minwalla and Motl are full-time string theorists and Randall and Arkani-Hamed do more phenomenological work, work whose justification is often given in terms of string theory. This just leaves Georgi remaining, and at the moment he has his hands full dealing with the fact that the president of Harvard is a sexist buffoon.

For Vafa to accomplish this undoubtedly took some single-minded dedication to furthering the interests of string theory and thwarting its opponents, but now that string theory so overwhelmingly dominates the field, it’s pretty disturbing to see him continuing to behave like a complete fanatic. I’ve been told that after Brian Greene’s Nova TV show about string theory came out, Vafa was heard to say that he didn’t care if it was any good; as far as he was concerned anything that promoted string theory was great. He’s quoted in the article as saying

“Theoretical developments have indicated string theory is a very important part of physics,” Vafa said. “It has already proven foolish. It’s past the point.”

I’m guessing there’s a typo here, one assumes he doesn’t mean that string theory is foolish, but that opposition to it is. He completely ignores the argument that string theory has not predicted anything and thus is not science, calling people who make this argument “childish”. His arrogant attitude towards those who don’t believe what he does is pretty breath-taking, matched only by that of his younger colleague Lubos. He finally dismisses the whole BU physics department with the logically incoherent:

“I think they are doing a disfavor to BU. I don’t want to pass judgment, but not having a string theory group puts [BU physics] out of first rate in my opinion.”

I think he does want to pass judgement and already has. If you’re a theorist who might someday have to deal with him as someone evaluating your grant proposal, deciding whether to hire your student, etc., do you think you might think twice before making a “childish” or “foolish” public comment about what is going on in string theory these days?

There’s a new TV show called “NUMB3RS” starting tonight, whose main character is a mathematican named “Charlie”, who solves crimes using mathematics. His motto is “Everything is Numbers”.

A secondary character is “Larry”, a Caltech physicist working on 11d supergravity. In one scene he shows up trying to get mathematical help from Charlie, whose graduate student sneers at him “Why don’t you do your own mathematics, like Ed Witten or Feynman?”.

Robbert Dijkgraaf is about the most lucid expositor around on the topic of what now goes under the name “topological strings”. This week he’s been giving the Coxeter Lectures at the Fields Institute in Toronto, and the slides and audio of his introductory talk are now available on-line. I hope there will be similar materials for his other, more detailed talks.

Last week the Fields Institute hosted a workshop on topological strings and the talks are on-line, although in many cases just the audio of the talk is available, which is pretty hard to follow.

Today’s Guardian has an article by a writer who recently visited the Institute in Princeton to talk to Witten and others there about string theory. The author of the piece makes the obvious analogy between Witten and Einstein, and asks the string theorists about Einstein’s 20-year misguided and failed attempt to unify gravity and electromagnetism during his years at the IAS. String theory and Einstein’s failed program get further identified by the author’s claim that if Einstein were alive today he would be working on string theory, and by a quote from Seiberg that “Being in the place where Einstein was is clearly an inspiring idea.”

Seiberg also has something very true to say:

“Most string theorists are very arrogant,” says Seiberg with a smile. “If there is something [beyond string theory], we will call it string theory.”

Witten’s attitude towards string theory seems to remain unchanged, he’s quoted as saying:

“Critics of string theory say that it might be too big a step. Most physicists in other fields are simply agnostic and properly so,” says Witten. “It isn’t an established theory. My personal opinion is that there are circumstantial reasons to suspect that it’s on the right track. ”

His recent work on twistor string theory is mentioned, including the fact that there was a workshop at Oxford last week on the subject. About this, the writer reports

“Witten is not convinced yet. ‘I think twistor string theory is something that only partly works,’ he says.”

I wonder exactly what he meant by that. What’s the part of twistor string theory that he thinks doesn’t work?

Most new preprints in mathematics and physics these days are posted on the arXiv, but every so often I run into interesting new things worth reading that haven’t appeared there for one reason or another. Here are some recent examples:

Some lecture notes on Lie algebras by Shlomo Sternberg. Lots of topics covered I haven’t seen anywhere else, especially the material on the relation to Clifford algebras and the Kostant version of the Dirac operator.

Lecture notes by Constantin Teleman about his recent work on topological field theories and the Gromov-Witten theory of BG, the classifying space of a group. These are notes from talks given at Gregynog, Goettingen, and Miami. I confess that, like a lot of Teleman’s work, I have trouble figuring out exactly what he is up to, but it looks quite interesting. I wish he and Dan Freed and Mike Hopkins would get around to finishing their paper on “K-theory, Loop Groups, and Dirac Families” that Teleman has been advertising as “coming soon” for quite a while…

David Vogan has an interesting draft of a review of A. A. Kirillov’s book on the orbit method in representation theory. This is the most fully developed version of what is sometimes known as “geometric quantization”. Vogan also has some notes from his lectures this past year on “Unitary representations and complex analysis” which include material on the Borel-Weil theorem and its generalizations.

Nikita Nekrasov has some Lectures on Nonperturbative Aspects of Supersymmetric Gauge Theories and a written version of his 2004 Hermann Weyl Prize lecture.

Eckhard Meinrenken has a a nice expository article on the de Rham model for equivariant cohomology.

For some interesting comments by Nima Arkani-Hamed about his model-building activities, followed by some of my own, take a look here.

Update: Jacques Distler has some comments on the Arkani-Hamed et. al. paper.

The world of particle physics web logging expanded by about an order of magnitude today, as a new web-site called Quantum Diaries came on-line. The idea seems to be to celebrate the 100th anniversary of Einstein’s remarkable 1905 papers by getting 25 physicists from around the world to set up web logs so people can follow what they do during 2005.

Most of the participants are experimentalists, with just three theorists as far as I can tell. The theorists are John Ellis of CERN (see here for a story about him), Stephon Alexander of SLAC, and Jochen Weller of Fermilab.

Interestingly, all three of the theorists are spending at least part of their time working on cosmological or astrophysical topics, which gives you some idea of where the field is headed. Also, none of them are working on string theory at the moment, which also gives you some idea of where the field is headed.

As a completely unrelated aside, today I came upon the web-site of Brian Powell, a graduate student of Will Kinney’s at Buffalo studying cosmology. He’s more pro than anti string theory, but irreverently funny. His comment that “many people criticize string theory because it’s sort of becoming fashionable to do so” warmed my heart. On the other hand, the fact that he links to something I wrote about Witten’s talk at Santa Barbara with the terms “Witten gets socked in the groin” kind of upsets me.