Not Even Wrong

Yesterday at the KITP in Santa Barbara, George Johnson gave a second talk and led a discussion on the subject of the “String Wars”. The rather remarkable first session was discussed here, here and here. This time people were much better behaved, and the main topic was the media coverage of physics in general, and the past history of the media interest in string theory, and what effects this might have had.

Johnson has put on his web-site copies of various articles from the NYTimes about string theory. The first mention of superstrings was in a piece by Walter Sullivan back in May 1985, just a few months after the “First Superstring Revolution” really got going. This piece included cautionary comments from C.N. Yang about the lack of even “a single experimental hint” and from Michael Green that “I’ve seen many bandwagons come and go.” Interestingly, already at this time the main suggested test of string theory was astrophysical or cosmological, with the Times referring to a recent Nature article about the possibility of seeing effects of the “shadow matter” that one gets from the other E8 in the E8 x E8 model popular back then (and still popular to this day).

Much of the KITP discussion concerned what effect news stories and popular books promoting string theory have had, with several people noting that they think they have been responsible for the large number of students they have seen wanting to do graduate work in string theory. Someone in the audience also pointed out that the continual use of the modifier “super” seems to get people’s attention, with students showing up wanting to study “supersymmetry” even though they didn’t know what it was, and it was much harder to get them interested in, say, “diffractive scattering.”

The latest Nature Physics has a fairly sensible editorial (Tied Up With String?) about the string theory controversy. Popular promotion of string theory continues today at Stanford, where the Wonderfest Festival of Science is featuring Raphael Bousso and Leonard Susskind discussing “Is the World Made of Strings?”

This week in Honolulu there’s a major particle physics conference going on, a joint meeting of the Division of Particles and Fields of the APS, and the Japanese Physical Society, called the Joint Meeting of Pacific Region Particle Physics Communities. Slides from the talks have started to appear here.

The conference is huge, with hundreds of talks (for some reason, attending a conference in Hawaii seems appealing to many people), and I haven’t had time to look at more than a few of them. Barry Barish gave a talk on international cooperation in HEP, Dave Schmitz one about the status of MiniBoone, which is “in the endgame” of a blind analysis of their neutrino experiment, with the black box containing their results to be opened in the not too distant future.

Lots of talks about string theory, including a plenary talk by Polchinski partly about AdS/CFT and attempts to use it to get information about QCD, partly about the landscape and string vacua. There was also a remarkable talk by Wati Taylor entitled Can String Theory Make Predictions for Particle Physics? Taylor begins by noting that “If we could do experiments at greater than 10¹⁹Gev, answer would probably be Yes”. “Probably” is different than the usual claims about this… His summary of the current state of string theory and particle physics goes like this:

• String theory need not make predictions for particle physics below 100 TeV
• We can’t define string theory yet
• The number of suspected solutions is enormous, and growing fast
• Nonetheless, constraints on low-energy physics correlated between calculable corners of the landscape may lead to predictions
• If not, probably need major conceptual breakthrough to have any possibility of predictivity for low-energy particle physics
• Raison d’etre for string theory: quantum gravity

I don’t know why he chose 100 TeV here, presumably just because it is probably an upper-bound on the likely energy scales particle physicists will be able to explore during the lifetimes of anyone now living. He could just as well have picked a much higher number. The only hope he sees for getting any kind of prediction using current versions of string theory is by finding correlations between things like numbers of generations and gauge groups when you examine large numbers of string vacua (this is similar to the conclusion reached by Michael Dine, described here). In work with Michael Douglas, he has found no evidence for this. Taylor also explains that the standard 10⁵⁰⁰ number often given for the number of string vacua seems to be a dramatic underestimate, and that it is even quite possible that the number is infinite when one takes into account non-geometric compactifications. Fundamentally, his conclusion seems to be that there is only a vanishingly small hope remaining of getting any predictions about particle physics out of string theory, so it has to be sold purely as a theory of quantum gravity, unless a miracle happens.

Taylor does make the case that string theory has found potential uses not in unification, but in studying strongly coupled gauge theory (AdS/CFT) and in suggesting new structures to try out in model-building. But at this point, he characterizes low energy physics predictions from string theory as unlikely, their appearance would just be an “unexpected bonus”. So, I guess the answer to the question of his title is basically “No”. Despite this, he does end by advertising the String Vacuum Project and listing the 17 prominent theorists who are asking the NSF to fund it.

From the “First Superstring Revolution” on, there have always been skeptics, even though they often were not very vocal. Perhaps the most well-known piece of such criticism was Paul Ginsparg and Sheldon Glashow’s Desperately Seeking Superstrings, which appeared in the May 1986 issue of Physics Today. I recently became aware of some other similarly critical articles by Noboru Nakanishi, and copies of them have been made available to me. They are:

Comments on the Superstring Syndrome (also from May 1986)

“Superstring Theory” Syndrome (published in the popular magazine “Parity”, September 1986)

Can the superstring theory become physics? (January 1993)

This last paper claims that “the bubble of superstring theory has … bursted”, which, in 1993, was rather premature.

The main argument generally given for working on string theory is that it’s the only way to get a finite theory of quantum gravity. One often hears claims that gravity can’t be quantized using QFT, that string theory is needed to “smooth out the violent space-time fluctuations at the Planck scale”, or some such explanation for the inherent non-renormalizability of quantum field theories of gravity. From the earliest days of their study, it was hoped that supergravity theories would have better renormalizability properties, with the maximally extended supergravity, N=8 supergravity, the most likely to be well-behaved.

For years the general belief has been that N=8 supergravity is non-renormalizable, based on the existence of possible counterterms at high enough order. The problem has always been that calculating the coefficients of these counterterms is too difficult, so one cannot be sure that one would not get zero if one actually did the calculation. Last year I wrote here about a talk by Zvi Bern in which he mentioned that twistor space methods for doing these kind of calculations were giving indications that these coefficients might be zero. Tonight there’s a new paper out by Green, Russo and Vanhove suggesting the same thing. Their arguments involve M-theory and consistency conditions relating supergravity and the low energy limit of 10-d superstring theory.

It would be quite remarkable if it turns out that this work by Michael Green, using string theory and M-theory techniques, ends up shooting down the main argument for why one has to abandon QFT if one wants to do quantum gravity.

Update: Next month at UCLA there will be an entire workshop devoted to this question, entitled Is N=8 Supergravity Finite?

Seed has a new article out by Stephen Ornes, called The Proof is in the Blogging, about the way the story of Penny Smith’s solution to the Navier-Stokes problem played out here. I’m quite fond of the photo included in the Seed article.

I’m not sure there’s anything more to be said about the Navier-Stokes story. One of my colleagues pointed out that mathematics is one of very few subjects in which bringing together a bunch of people with opposite views on what is true generally leads to one or more of them agreeing that they were wrong.

There’s also a short article about this on Slashdot. Taking advantage of the arXiv trackback mechanism, the author found the discussion of this on Lubos’s blog. I was going to take the opportunity to complain about the arXiv censoring links to this blog, but it turns out in this case there is one there. The ways of the arXiv are endlessly mysterious, I have no idea what their trackback policy is these days.

Maybe it’s also relevant to mention that for some reason the hot news retailed here about the proof of finite generation of the canonical ring is not attracting the kind of attention indicated in the Seed picture.

This week’s Science News has a quite good article about the string theory controversy by Peter Weiss, unfortunately available on-line only to subscribers. The title is “Fit to be Tied: Impatience with string theory boils over”. There’s nothing much in the article that will surprise anyone who has been following this story here. It includes some accurate quotes from me and some from Lee Smolin, with the string theorists represented by Zwiebach, Polchinski and Strominger.

Polchinski claims that experiments will soon probe some elements of string theory, promoting the possibility that the LHC will observe extra dimensions. Zwiebach points to work on black holes: “In string theory, the black hole can be seen as built from strings and branes. It’s a spectacular insight.” Strominger on the one hand is quoted as finding it inappropriate that Smolin and I are criticizing how string theory research is conducted, while also saying he thinks that the way string theory has been promoted has given the public the wrong impression: “I’ve felt for a long time that the general public’s impression of what string theory had accomplished and how much of it was correct was too positive.”

Earlier this month there was a workshop on twisted K-theory held at Oberwolfach. Here is a report, also slides from a talk there by Greg Landweber about the Freed-Hopkins-Teleman theorem. Freed is giving a course on the subject this fall, and Hopkins is giving a series of lectures about TQFT in Gottingen this week. Urs Schreiber has reports on the lectures here and here. Also at the n-category cafe is an advertisement by John Baez for the work of my new Columbia colleague Aaron Lauda on TQFT, which I’ll second here. For yet more on TQFT, see notes by Kevin Walker here, and the book by Bakalov and Kirillov, an early version of which is on-line.

Last week in Paris there was a conference dedicated to Joel Scherk, celebrating 30 years of supergravity.

There’s an interesting interview with Alain Connes on the French TV network ARTE here. For his recent work on non-commutative geometry and the standard model, see this preprint, and talks here from the on-going workshop at the Newton Institute in Cambridge.

The last few weeks have seen the appearance of two papers giving very different proofs of a quite important result in algebraic geometry, resolving a question that had been open for a very long time, and in the process helping to make progress in the classification of higher dimensional projective algebraic varieties. Readers should be warned that this doesn’t have anything to do with physics, and my knowledge of this kind of mathematics is highly shaky, so I’m relying largely on second-hand information from people much better informed than myself.

The theorem in question concerns the “canonical ring” of a smooth projective algebraic variety X, which is the graded ring R(X) defined by
$$R(X)=\oplus_{n=0}^\infty H^0(X, nK)$$
Here K is the canonical line bundle (top exterior power of the cotangent bundle) of X, nK is its n’th tensor power, and $H^0(X, nK)$ is the space of holomorphic sections of the bundle nK. This is also called the pluricanonical ring.

The new theorem says that this graded ring is finitely generated, and this implies quite a few facts about projective algebraic varieties of any dimension. In particular it implies the main goal of the “minimal model program” (also known as the Mori program) for classifying higher dimensional algebraic varieties.

A proof of this theorem was claimed back in 1999 by Hajime Tsuji, but it appears that there are problems with this proof. The arXiv preprint went through many revisions, but was never refereed and published. A couple weeks ago, a group of four algebraic geometers (Caucher Birkar, Paolo Cascini, Christopher Hacon and James McKernan) posted a preprint on the arXiv claiming a proof. Yesterday, Yum-Tong Siu, a well-known complex geometer from Harvard, posted another preprint, giving a very different, more analytical, proof of this theorem. Siu notes that he has been lecturing on this proof for over a year, first at last year’s Seattle conference on Algebraic Geometry.

The mathematicians involved in creating these two proofs are well-known experts, and it seems likely that both proofs are correct. Given that there are two of a quite different nature, it now seems extremely likely that this theorem has been proved.

For more detailed explanations of this result and its implications, I’m afraid that you’re likely to require someone who knows a lot more about algebraic geometry than I do. Perhaps some of my more expert readers here can help out.

Yesterday at the KITP Michael Dine gave a very good survey talk on Prospects for a String Theory Phenomenology. It’s pretty much hype free, has a much more realistic point of view than most talks on string phenomenology that I’ve seen, and gives a good idea of the current state of the subject.

Dine claims that almost all string theorists now accept the existence of flux vacua, although only some have adopted the anthropic landscape philosophy of Susskind et. al. He describes some string phenomenologists as closing their eyes to the problems represented by the large number of these vacua, and just working on some of the more tractable examples in the hope that something will turn up that will allow them to make some connection to the real world. He himself is convinced by the Denef-Douglas argument that even identifying a single vacuum state with sufficiently small cosmological constant is impossible, so that one has to make statistical arguments. He tries to have some optimism that perhaps this statistical study will allow one to make some kind of prediction, perhaps about whether the scale of supersymmetry breaking is low or high, although so far this has turned out to be impossible.

The discussion at the end of the talk is very interesting, with Dine acknowledging that there are lots of reasons he may be barking up the wrong tree and saying that he would be happier if this turned out to be the case. He quotes Witten as telling him that what he is doing can’t work, that there isn’t much point in trying to do the calculations he is trying to do because:

A.: “You are probably not going to succeed”, and

B: “If that is all you can do it would be a great disappointment. We have this beautiful theory and we are going to get everything out of it” [i.e. it would be unpredictive].