Not Even Wrong

Alexander Polyakov is one of the most prominent figures in theoretical physics and one of the most well-known string theorists at Princeton. He has written a review of his career and of his efforts to understand the relation between gauge theory and string theory. His penultimate paragraph goes as follows:

“In my opinion, string theory in general may be too ambitious. We know too little about string dynamics to attack the fundamental questions of the ‘right’ vacua, hierarchies, to choose between anthropic and misanthropic principles, etc. The lack of control from the experiment makes going astray almost inevitable. I hope that gauge/string duality somewhat improves the situation. There we do have some control, both from experiment and from numerical simulations. Perhaps it will help to restore the mental health of string theory.”

Seems to me he’s saying that, while using string theory to understand gauge theory is sensible, those claiming that it provides a theory of everything have gone nuts. I wonder what his colleagues at Princeton think of this.

Hawking gave his widely anticpated talk in Dublin today and reports are on CNN and all sorts of other places in the media. Sean Carroll has managed to get ahold (via Dennis Overbye of the New York Times) of a transcript.

Here’s the part where he summarizes his argument:

“I assume the evolution is given by a Euclidean path integral over metrics of all topologies. The integral over topologically trivial metrics, can be done by dividing the time interval into thin slices, and using a linear interpolation to the metric in each slice. The integral over each slice, will be unitary, and so the whole path integral will be unitary.

On the other hand, the path integral over topologically non trivial metrics, will lose information, and will be asymptotically independent of its initial conditions. Thus the total path integral will be unitary, and quantum mechanics is safe.”

His argument is in Euclidean quantum gravity, which he describes as “the only sane way to do quantum gravity non-perturbatively”, something which some might disagree with. What he seems to be arguing is that, while it is true you get information loss in the path integral over metrics on a fixed non-trivial black hole topology, you really need to sum over all topologies. When you do this you get unitary evolution from the trivial (no black hole) topology and the non-trivial topologies give contributions that are independent of the initial state and don’t contribute to the initial-final state amplitude.

I guess what this means is that he is claiming that, sure, if you knew you really had a black hole, then there would be a problem with unitarity, but in quantum gravity you don’t ever really know that you have a black hole, you also have to take into account the amplitude for not actually having one and when you properly do this the unitarity problem goes away.

He has some proposal for doing some kind of calculation that implements his proposal using the AdS/CFT correspondence.

My copy of the proceedings of the conference in honor of Graeme Segal’s 60th birthday finally arrived and I’ve been spending some enjoyable time reading parts of it. To me, the most interesting contributions were the ones by Ben-Zvi and Frenkel, Dijkgraaf, Moore, Stolz and Teichner, Teleman and Witten. Unfortunately, Dijkgraaf’s beautiful paper about how matrix integrals give you Gromov-Witten invariants of Calabi-Yau manifolds doesn’t seem to be available on-line. Neither is Witten’s very interesting paper, which is about explaining the SL(2,Z) symmetry seen in N=4 SSYM in four dimensions in terms of the existence of a six-dimensional superconformal theory.

The Stolz and Teichner paper is quite interesting . They are pursuing the idea that conformal field theories provide geometrical representatives of elliptic cohomology classes. Segal and Mike Hopkins worked on this a bit in the late 80s, with no conclusive results. Recently Hopkins has reformulated the whole elliptic cohomology story in terms of a new cohomology theory he calls “topological modular forms”. He gave a beautiful series of talks about this at the Segal Conference; this isn’t written up in the proceedings, but was for the 2002 ICM. For a more expository version of the ideas of Stolz and Teichner, see Teichner’s survey talk at a conference in Santa Barbara last summer.

Finally, the proceedings volume contains Segal’s wonderful unfinished manuscript “The Definition of Conformal Field Theory”, together with nine pages of very interesting comments about what he was trying to do then, what he would do differently now, and what had kept him from finishing the manuscript. The main problem seems to have been that he was unable by his methods to explicitly construct the “modular functor” that one should get out of WZW models, so for this reason the crucial chapter 11 on WZW models remains unwritten.

His comments begin with:

“The manuscript that follows was written fifteen years ago. On balance, though, conformal field theory has evolved less quickly than I expected, and to my mind the difficulties that kept me from finishing the paper are still not altogether elucidated.”

Two new books from Cambridge that are now available:

A First Course in String Theory by Barton Zwiebach, based on a course on string theory for undergraduates taught at MIT. It’s available for \$42 at Barnes and Noble, sales rank 565, for \$60 at Amazon, sales rank 13,559. The whole idea of trying to teach a very speculative theory that hasn’t really worked and which is based on 2d quantum field theory to undergraduates seems to me to be utter lunacy. But maybe I’ll even buy a copy.

Topology , Geometry and Quantum Field Theory, the proceedings of a symposium that I went to at Oxford in 2002 in honor of Graeme Segal’s 60th birthday. This conference had some wonderful talks and I’m looking forward to reading many of the contributions. Supposedly it also contains Segal’s manuscript “The Definition of Conformal Field Theory”, which has been circulating in samizdat for years. My copy (which like many others contains the hand-written notation “Do Not Copy” on the front) is falling apart, yet another reason why I just ordered the book, even though it is \$90. The story I heard is that Segal didn’t want his manuscript reproduced, but finally agreed on the condition that it not be re-typeset, but appear exactly as in the original, so that it would be clear that it was still something preliminary and tentative, with no corrections or improvements made since he wrote it.

Witten is lecturing at a conference in Crete this week and some of his transparencies are already online. He is talking about perturbative gauge theory amplitudes and the idea of interpreting them in terms of strings in twistor space. He motivates this by noting that AdS/CFT is useful for understanding gauge theories at large g^2N, but at short distances asymptotic freedom implies g^2N is small and to understand gauge theory in terms of strings you need to do so for all g^2N. He warns “I can’t promise that what I’ll explain will turn out ot be useful in a string description of QCD, but at least I’ll tell you interesting things about perturbative gauge theory!”.

For something completely different, the latest on the Landscape is that, at least this week it predicts low energy supersymmetry, maybe.

There a new article on Slate about string theory and my colleague Brian Greene. Also some commentary about it on David Appell’s weblog Quark Soup.

Michael Atiyah and Graeme Segal have a new foundational paper out on twisted K-theory. It doesn’t have too many examples or applications, but lays a rigorous foundation for a certain point of view on the subject. Section 5 is the one quantum field theorists should pay attention to, it explains the relation to the fermionic Fock space. For a more explicit construction relating QFT to twisted K-theory, besides the papers of Freed, Hopkins and Teleman, one can look at “Gerbes, (twisted) K-theory, and the supersymmetric WZW model” by Jouko Mickelsson.

Throughout the mid-to-late 80s, the NSF and other organizations would periodically issue alarmist reports about an impending dangerous shortage of scientists and engineers in the U.S. These projections for shortages turned out to be utter nonsense, as anyone who looked at the situation honestly could have foreseen. By the early 90s, instead of a shortage, the bottom dropped out of the employment market for scientists. In the math department here I saw a large number of very good graduate students and post-docs leave the field because there were no jobs for them.

Particle theory is a field in which the job market has been varying degrees of awful since about 1970. One might argue that while this is tough on young particle theorists, it means that the few who get jobs will be truly outstanding and the subject will flourish. The problem with this argument is that particle theory has seen extremely little progress since the mid-70s, about the time that one would expect the effects of the tight job market to be seen. The main reason for this is that the standard model is just too good, but one could plausibly argue that the evidence is that a very tight job market is bad for the field. Good people don’t go into it; those that do and survive do so by not working on anything too ambitious, because it could easily fail and they’d be out on the street.

Mathematics is a much more normal job market than particle theory, but there still have always been a lot more Ph.D.s than jobs where they can use their talents. The job market in math was terrible in the early-to-mid nineties, got better in the late-nineties and is not so bad now. Our students seem to be doing relatively well at getting jobs. Budgets are tight, especially at state universities, but a lot of people hired during the 60s are finally starting to retire.

The NSF is now at it again, with its National Science Board issuing a glossy report entitled An Emerging and Critical Problem of the Science and Engineering Labor Force. A good article in the Chronicle of Higher Education reports on this, but also has a lot of information debunking the report.

Why does the NSF repeatedly engage in this kind of alarmism and dishonesty? If you take a look at the membership of the National Science Board, you’ll find no young scientists, but a lot of university and NSF administrators, corporate executives, and senior professors. All of these people have a large vested interest in flooding the scientific labor pool in the U.S. so that it will provide a lot of cheap labor. The NSF gets much of its funding from Congress by emphasizing its role in training scientists, so of course it wants to claim that more of this needs to be done. Universities and corporations want lots of new Ph.D.s so they can get the best ones to work for them for peanuts. Universities want lots of grad students to provide cheap labor as TAs. Senior professors, at least in the experimental sciences, want lots of grad students to staff their labs cheaply. These people all seem to firmly believe that a system that produces huge numbers of underemployed and badly paid young scientists is the best thing for science and for the U.S. as a whole. In fact, it is just the best thing for their personal interests.

The buzz is that Hawking has a new idea about how to resolve the “Black Hole Information Paradox”, the well known incompatibility between standard ideas about black holes and the unitary time evolution of the wave function that is fundamental to quantum mechanics. Evidently Hawking has asked to give a talk about this at GR17, a big conference on general relativity that will be held July 18-23 in Dublin.

The abstract for his talk goes like this:

“The Euclidean path integral over all topologically trivial metrics can be done by time slicing and so is unitary when analytically continued to the Lorentzian. On the other hand, the path integral over all topologically non-trivial metrics is asymptotically independent of the initial state. Thus the total path integral is unitary and information is not lost in the formation and evaporation of black holes. The way the information gets out seems to be that a true event horizon never forms, just an apparent horizon.”

I can’t tell exactly what that means either, so I guess we’ll have to wait for the talk. My own prejudice about quantum field theory is that the relation between the Euclidean and Minkowski space formulations of quantum field theory is actually much more interesting and subtle than people think. It’s not just a technical trick. So I’ll be interested to see what Hawking has to say about this.

Something else at the conference that may be interesting will be Sir Roger Penrose’s public talk entitled “Fashion, Faith and Fantasy in Modern Physical Theories”. Guess what he is referring to by “Fashion”.