Not Even Wrong

The KITP at Santa Barbara is holding a conference on QCD and String Theory this week, and the talks have started to appear online.

Of the ones I’ve taken a quick look at so far, there doesn’t seem to be any obvious recent progress on the 30-year old main question that everyone would like the answer to: can one find a reliable analytical technique for dealing with QCD in the infrared regiion where the effective coupling is strong? The best hope for this in recent years has been the AdS/CFT correspondence, but after seven years the state of the art there still seems to be a long ways from solving the problem one wants to solve (although it does give solutions to other problems). I’m looking forward to seeing what some of the later talks will have to say, including Larry Yaffe’s one tomorrow on “Large N gauge theories: old and new”.

Martin Veltman gave a colloquium talk at Fermilab two weeks ago and, as usual, had some very provocative comments to make. At the end of his talk he made the claim that the only thing astrophysics has contributed to particle physics is information about the number of neutrinos (from Helium abundance observations). He claims “Apart from this, Astrophysics is so far useless to us.”

He then gave some purported data about how particle physicists really felt about the impact of astrophysics and cosmology on their field. His slides say:

“Question put to many particle physicists: Do you feel that astrophysics and particle physics are joined at the hip?

Response:

Refusing to respond on the grounds that it is an obscene proposition (99.9%)
Do not know what you are talking about (9.671%)
Undecided (rest)

Questions put to particle experimenters:

Your experiment is justified by claiming that it will tell us about the first seconds of the big bang. Do you agree?

Response:

No (98.312%)
Do not know what you are talking about (1.671%)
Undecided (rest)

Do you feel that we need a new machine (linear collider) because it can be used to discover dark matter (dark energy)?

Response:

No (98.312%)
Do not know what you are talking about (1.671%)
Is this related to the death star of Darth Vader? (3%)
Undecided (rest)”

I think Veltman has a very good point. The particle physics community seems to have decided to try and sell the public on supporting particle physics, specifically a new linear collider, by claiming that such a machine will “solve the mystery of dark energy”, find “extra dimensions of space”, and tell us “how the universe came to be” (see for instance the HEPAP Quantum Universe report). This all sounds very sexy, but there’s no good reason to believe that a linear collider will do any of this. Maybe this is the right way to sell the linear collider, but personally I’m rather uncomfortable with this level of hype and wouldn’t want to be the one testifying under oath before Congress about this.

Veltman also comments that “It appears to me that the only viable solution is that this machine will be located in the US”, but given the massive deficit the Bush administration has created and current political realities, I find it hard to believe we’ll see the kind of budget increases for particle physics that would be required to make this happen anytime soon.

The Jacobian Conjecture is one of the most well-known open problems in algebraic geometry. It now seems that a proof has been found by Carolyn Dean of the University of Michigan, for the case of polynomials in two complex variables (for more variables, many people believe it is not even true). For more information about this, see Graham Leuschke’s weblog.

Dean hasn’t published any papers in almost 15 years and is nominally a lecturer in mathematics education at Michigan. There have been many false proofs of this conjecture over the years, and if this one holds up it will be quite a story. The paper doesn’t seem to be publicly available yet, but Dean will be lecturing on the proof at Michigan next month. One of the experts in the field, Mel Hochster, has gone over it carefully and is convinced it is correct. The rumor I hear is that it has been submitted for publication to the Journal of the American Mathematical Society.

Update: There’s an announcement of Dean’s talks posted on sci.math.research.

Update: Someone wrote in with a comment to another post pointing out that Dean has found a hole in her proof. For some more information about this, go here.

At his talk last year at the conference in honor of Gelfand’s 90th birthday, Atiyah posed the question of whether there is a quantum field theoretic explanation of why the coefficients of the Jones polynomial are integers. Witten’s Chern-Simons-Witten theory is a 3d QFT that computes the Jones polynomial (a topological invariant of knots or links inside a 3d manifold), but gives no obvious reason the coefficients should be integral.

One thing about the Chern-Simons-Witten story that has always bothered me is that, unlike his other TQFTs, this one is not of a homological nature. In the other TQFTs, the Hilbert space is finite dimensional because there are fermionic variables which cause cancellations such that only the homology of some complex contributes to the observables. To make any real sense of the idea of a path integral whose Lagrangian is the Chern-Simons functional, one has to do something like add a Yang-Mills term, then take a limit. By doing this one can move all but a finite part of the usual gauge theory Hilbert space off to infinite energy. It would be very interesting if there were a version of the theory which instead worked homologically like other TQFTs.

A hot topic in low dimensional topology recently has been the notion of “Khovanov homology”, which associates to a knot a complex whose homology is the Jones polynomial. For an introduction to Khovanov homology, see papers by Dror Bar-Natan (a mathematician who was a student of Witten’s) or Jacob Rasmussen. Bar-Natan has a lot of other material about Khovanov homology on his web-site.

One way of answering Atiyah’s question would be to find a 4d TQFT whose Hilbert space is the Khovanov homology of the boundary. Maybe there is some sort of gauge-theory based QFT which generalizes the Chern-Simons-Witten theory and computes Khovanov homology. But after consulting the local expert on these things (Peter Ozsvath), it seems that no one knows whether it is even possible to reformulate Khovanov homology in any sort of gauge-theoretical terms. The only known definitions of it are kind of like the pre-Witten skein relation definitions of Jones polynomials. They are based on working with a projection of the knot onto two-dimensions.

A couple weeks ago Sergei Gukov gave a talk in the math department at UCSD with the title “Topological Invariants and Khovanov Homology”, and perhaps his work has some relation to the above speculations.

Gukov is also the co-author of a paper that just appeared on the arXiv entitled “Topological M-theory as Unification of Form Theories of Gravity”. Like M-theory itself, it appears that no one knows what “topological M-theory” is, but it is supposed to be some sort of seven-dimensional theory that is related to topological strings on 6d Calabi-Yaus in much the same way M-theory is a conjectural 11d theory related to 10d superstrings. Lubos Motl has even more questions about this than I do.

Shamit Kachru gave the physics colloquium at Rutgers yesterday. His title was “The Theory of More Than Everything” and I heard from people who attended that he was promoting research into the “Landscape” as a new model of how to do theoretical physics, especially cosmology.

I was down there today and heard two talks in the mathematical physics seminar, by Abhay Ashtekar and Tom Banks. Ashtekar’s talk was a standard exposition of a few of the basic ideas of loop quantum gravity, also reviewing an attempt to apply these ideas to cosmology. The talk by Banks was titled “Triumphs and Travails of String Theory”. The first hour was about the triumphs, giving a pretty standard survey of the supposed accomplishments of string theory. Banks emphasized the importance of supersymmetry, and described string theory as not quite background independent, but depending only on a choice of “asymptotic background”. He dealt with matrix models, holography, BPS states, dualities, getting gauge bosons out of string theory, and AdS/CFT.

His talk contained quite a lot of content, unlike some promotional talks of this kind, but it did come off a bit like an hour-long infomercial (“And, there’s even more! It slices, it dices, it ….”). The last five minutes were devoted to the travails of string theory, of which, according to Banks, there is really only one (although he did mention that the lack of observed supersymmetry is also a problem). The one travail is the fact that the cosmological constant seems to be positive, so the universe is de Sitter, not anti de Sitter or flat. This creates well known problems with defining an S-matrix. He went on to explain the “Landscape” idea with its de Sitter states that are only metastable, saying this “leads to a new philosophy of doing physics that many are exploring”. He didn’t seem interested in directly criticizing this new philosophy, but did end by promoting his own, different, ideas about how to deal with the cosmological constant problem.

During the question session afterward, someone asked if there was any overlap between loop quantum gravity and string theory. After some hemming and hawing by the speakers, Michael Douglas spoke from the audience, saying that since string theory was really 20 or so different kinds of approaches to quantum gravity, it was quite plausible that LQG was another related one.

A correspondent points out that this month’s Physics Today has a couple articles about ethical issues involved in how physics research is conducted in the U.S.

Most of this doesn’t really apply to the kind of research I know best, theoretical research in physics and research in math. One main issue considered is the trustworthiness of experimental data, and as far as I can tell, in elementary particle physics the data is quite trustworthy. Since the collaborations that produce these results are so huge, many people are involved in going over any published result of any interest, so even if someone were tempted to fake or manipulate data, it would be hard to get away with.

Another issue of concern is the treatment of young experimentalists, who are often overworked and under-recognized. But the situation of theorists is generally different. In most cases the problem for them is thesis advisors who ignore them, not ones who pay close attention to what they are doing and make them work too hard. There is a fundamental ethical problem in the treatment of young theorists by the physics community, that of producing far more particle physics Ph.D.s than there are jobs for. This creates a brutal situation for young people, while it is to some degree in the interests of those who are established in permanent positions to let this go on.

The main ethical problem in particle theory research these days, a fundamental lack of honesty in how the results of this research are evaluated, doesn’t seem to be addressed at all in the Physics Today articles.

Howard Georgi gave a colloquium at Fermilab last week, and the slides and video from his talk are now online. He has gathered quite a lot of interesting data about women in the various sciences at the undergraduate and graduate level, and he discusses his experiences at Harvard over the years as he became more aware of the problems experienced by women studying physics. As chair of the department and in other capacities, he has tried to understand why there are so few women studying physics, significantly fewer than in the other sciences, concluding that “Many of our women physics concentrators were trapped in an emotionally abusive relationship with the Harvard Physics Department!!!”. He also concluded that it was “past time to outgrow the hypermacho lone-ranger approach to physics”, and that this would make the field more fun for everyone.

The whole issue of why so few women study physics (and math) seems to me a complicated one since it is mostly about the very complex and tricky ways in which people deal with how others expect them to fit into certain behavior and roles appropriate to their gender. I don’t think the “emotionally abusive relationship” that Georgi describes the Harvard department as having with its students is limited to the female ones. While I can say that in many ways I very much enjoyed my time as an undergraduate there, the great majority of the faculty were less than friendly to the students (with Georgi a prominent exception), and the general level of social skills of both the faculty and many of one’s fellow students left a lot to be desired. According to Georgi, changes have been made to the culture of the place and it is much more encouraging of its students. This is part of a general trend at many US institutions, partly because of increased sensitivity to gender issues, partly just because the students are paying a lot more to be there than they used to, and their increased dollars get them increased attention and respect.

Then again, they now have Lubos Motl, so the Harvard department’s traditions of hyper-aggressive behavior have not totally been lost.

SLAC and Fermilab have joined forces and replaced their “FermiNews” and “Beam Line” publications with a new one called “Symmetry”. I like the title; it’s nice to see that the major US particle physics labs are supporting a publication about group representation theory.

One of the arguments often given for string theory is that it is somehow exceptionally “beautiful”. This has always mystified me, since that’s certainly not the way I would describe it. Over the years I’ve paid close attention whenever I see someone trying to explain exactly what it is about string theory that is so beautiful. Lubos Motl has just posted his own detailed answer to this question, something I read with interest.

As usual, Lubos is not exactly concise, so I won’t quote him extensively, but let me try and summarize his arguments for calling string theory beautiful, together with some of my own comments.

1. Symmetries are beautiful and just about every symmetry you can imagine gets used somewhere, somehow in string theory.

Even Lubos is not so sure of this argument, since he says ” I don’t really thing that we view symmetries as the most important reason why string theory is beautiful”. What is beautiful about symmetries is the way they constrain things. If your theory is based upon a simple symmetry principle (take for example gauge theory and the gauge symmetry principle), a huge amount of structure follows from a single, simple principle. String theory is not based on a simple symmetry principle, rather it is a complicated framework, into which you can fit all sorts of different symmetry principles. But because they are not fundamental, these symmetries don’t constrain the theory much if at all. This is very different than the standard model, where at a fundamental level the theory is built around a single symmetry principle, one that governs a large part of the structure of the theory and its physical predictions.

2. The way in which “miraculous” cancellations occur in string theory, constraining the theory by only allowing it to make sense for certain specific choices.

The most well known example of this is the way in which anomaly cancellation picks out 10 dimensions and SO(32) or E_8 times E_8 for the superstring. This was the main reason people got so excited back in 1984, when they thought that the anomaly cancellation principle would give them a nearly unique theory that could be used to make predictions. If the anomaly cancellation principle had picked out four dimensions and SU(3)xSU(2)xU(1), that certainly would have been a beautiful explanation of why the standard model is the way it is. In the standard model itself, anomaly cancellation for the chiral gauge symmetry does work in an impressive way. If you take just the leptons or just the quarks, you have an anomalous theory, but the anomalies of the one cancel those of the other.

In string theory, all anomaly cancellation does is pick out a much too large dimension of space-time and a much too large gauge group. You can certainly embed the standard model in this structure, but you could also embed just about anything you want in it because there is so much room. In the end you are stuck with some version of the “Landscape”, essentially an infinite number of different possibilities with no way to choose amongst them. The anomaly cancellation ends up providing very little constraint on what the structure of low energy physics looks like.

3. String theory is a unique theory that can predict everything about the physical world.

Lubos likes to go on about how unique and predictive string theory is. While I understand this is the dream of every string theorist, the reality of what they actually have is a long ways from what they hope is true. The vision of what they would like to be true may be beautiful, but the reality is something else. The reality is that there is no “unique” string theory that can reproduce the real world, just a dream that such a theory exists. And as for predictions of string theory, there are none. When Lubos says that “string theory predicts” things, what he really means is that if every thing he would like to be true actually were, then in principle you could predict things from string theory.

4. String theory manages to extend quantum field theory in a consistent way, something which is very non-trivial and the way this happens can be described as beautiful.

This seems to be Witten’s main argument these days for promoting the continued study of string theory and I have a certain amount of sympathy for it. There certainly is something of interest going on behind the complicated framework that people are studying under the name “string theory” and maybe it will someday lead to insight into something about physics, most likely the strong coupling behavior of gauge theories. But the fact that there is interesting structure you don’t understand doesn’t mean that this structure has anything to do with a fundamental unification principle for physics.

5. There are beautiful connections to new pure mathematical structures.

The relation of string theory to mathematics is a huge topic, and I’ll comment on it at length at some other time. In brief though, while I think string theory has been an utter disaster for theoretical physics during the past 20 years, it has lead to many interesting things in mathematics. However, most of these interesting things really come from 2d conformal QFT, and I would argue that it is QFT which is having a huge impact on mathematics, much more so than string theory. Witten’s Fields medal was for his work on the relation of QFT to math, not for anything he has done using string theory.