Not Even Wrong

Steve Miller pointed me to a fascinating interview with Jim Simons and C. N. Yang, available on YouTube here.

Simons tells the story of how he got kicked out of his job at the IDA in 1968 over his opposition to the Vietnam War, and ended up at Stony Brook as chair of the math department there. He and Yang collaborated on raising money to support anti-war efforts.

They describe how Yang went to Simons to try and find out about fiber bundles and what they might have to do with gauge theory. Simons started by referring Yang to Steenrod’s The Topology of Fibre Bundles, which Yang couldn’t make any sense of (Simons admits he never made it all the way through the book himself). This did in the end lead Simons and Yang to some real understanding of how vector potentials in gauge theory and connections on bundles were the same thing, with monopoles examples of topologically non-trivial bundles. Simons lectured at Stony Brook in 1975 on this, and a paper later that year by Wu and Yang included what became known as the “Wu-Yang dictionary” relating terminology in gauge theory and geometry. Singer learned about this soon thereafter when he visited Stony Brook, and went on to spread the news to Oxford, MIT and elsewhere.

Simons also describes what is going on with plans for the new Simons Center for Geometry and Physics, including some of the thinking that led him to decide to support this. The official ground-breaking ceremony for the new building there was held last week, you can follow construction progress here.

Strings 2009 is about three weeks away, and it will bring 450 or so string theorists to Rome. The topics of the talks at the Strings 200x conferences give a good idea of what the hot topics in the field are, and this year’s talk titles are now available. What’s big this year are scattering amplitudes, as well as the usual AdS5/CFT4 topics, supplemented by the more recently popular AdS4/CFT3. As far as phenomenology goes, the hot topic is definitely local F-theory models, with three separate talks on the subject.

One topic that is not hot is anything mathematical, with no research talks by mathematicians or Witten, and little about mathematically significant topics such as mirror symmetry. What also seems to no longer be hot is either string cosmology or the landscape. No cosmology, multiverse or Boltzmann Brains are to be found among the research talks, although Brian Greene will give a public lecture about the issue of possible multiple universes.

Last weekend I was up in Cambridge attending the conference in honor of Is Singer’s 85th birthday. Singer has had a very long and distinguished career in mathematics, much of it at MIT, where he arrived as one of the first Moore instructors back in 1950. Besides a wide range of purely mathematical contributions, Singer was responsible for bringing together mathematicians (including Atiyah) and physicists starting back in 1976, at first around questions related to instantons. He has run a joint physics and mathematics seminar for about a quarter century, at Berkeley while he was there, then back at MIT. Unfortunately, this past year will have been the last year of the seminar, partly due to Singer’s imminent retirement, partly due to a shift in the interests of Boston area physicists towards phenomenology and away from mathematics.

Jim Simons, an old friend and student of Singer’s, played an important role at the conference, as master of ceremonies at the dinner, and as a financial backer. Back in 1975 it was his lectures to physicists at Stony Brook that got Yang and ultimately Singer interested in the question of the relation of gauge theory to geometry.

While in Cambridge, I picked up a copy of a new book, Recountings, which has interviews with many MIT mathematicians (including Singer), and does a good job of portraying the history of the MIT math department over the past 50 years or so.

Of the conference talks I managed to get to, probably the best was that of Mike Hopkins, who gave a blackboard talk about the Kervaire invariant problem. This one was a lot more accessible than his talk last month at the Atiyah80 conference, where he unveiled his dramatic new results with Hill and Ravenel (more about this story here). In the MIT talk, Hopkins concentrated on explaining the background and significance of the problem, as well as giving some of the philosophy of the proof, which uses what he describes as a “designer” cohomology theory.

Some quick notes on a few of the other talks that I made it to:

HEPAP is meeting in Washington today, talks starting to become available here. Things are very different now than in past years, with huge budget increases for all areas of HEP at the NSF and DOE.

FQXI has awarded quite a few mini-grants, the list is here. They also have a new essay contest, on the topic What is possible and impossible in physics?

Some worthwhile expository mathematics pieces:

Motives—Grothendieck’s Dream
The Theory of Witt Vectors

At least one mathematician is a viscount and has a coat of arms.

Witten has a new paper on the arxiv entitled Geometric Langlands From Six Dimensions, an expository account of a rather special 6d superconformal theory and how its existence implies SL(2,Z) symmetry of N=4 SYM, and thus duality in geometric Langlands theory. He remarks that there isn’t a widely used name for this theory, calling it the “six-dimensional (0,2) model of type G”.

This week there’s a workshop on Topological Field Theories going on at Northwestern, with David Ben-Zvi lecturing on Topological Field Theory, Loop Spaces and Representation Theory. I hope he’ll soon follow his standard practice of putting notes up on his web-site.

Tomorrow I’ll head up to Cambridge for the weekend, to visit my brother and his family and to attend the Perspectives in Mathematics and Physics conference being held in honor of Is Singer’s 85th birthday.

Update: Notes from the Northwestern workshop are available here (from Evan Jenkins) and here (from Alex Hoffnung).

Update: David Ben-Zvi has posted notes from his talk and some others at the Northwestern workshop here.

The Spring 2009 IAS newsletter is out, available online here. It includes the news that the IAS is stealing yet another physics faculty member from Harvard, with Matias Zaldarriaga moving there in the fall.

The cover story of the newsletter is called Feynman Diagrams and Beyond, and it starts with some history, emphasizing the role of the IAS’s Freeman Dyson. It goes on to describe recent work on the structure of gauge theory scattering amplitudes going on at the IAS, emphasizing recent work by IAS professor Arkani-Hamed and collaborators that uses twistor space techniques, as well as Maldacena’s work using AdS/CFT to relate such calculations to string theory. Arkani-Hamed (see related posting here) says he’s trying to find a direct formulation of the theory (not just the scattering amplitudes) in twistor space:

We have a lot of clues now, and I think there is a path towards a complete theory that will rewrite physics in a language that won’t have space-time in it but will explain these patterns.

and explains the relation to AdS/CFT as:

The AdS/CFT correspondence already tells us how to formulate physics in this way for negatively curved space-times; we are trying to figure out if there is some analog of that picture for describing scattering amplitudes in flat space. Since a sufficiently small portion of any space-time is flat, figuring out how to talk about the physics of flat space holographically will likely represent a real step forward in theoretical physics.

One IAS member who is also working in this area is Emil Bjerrum-Bohr, a great-grandson of Niels Bohr, and the newsletter has an article about him and the various members of the Bohr family who have been at the IAS at one point or another.

For one more piece of news related to Feynman diagrams, Zvi Bern et al. have a new paper out where they explicitly construct the four-loop four-particle amplitude, for N=8 supergravity, and show that it is ultraviolet finite in both 4 and 5d. This provides yet one more piece of evidence for the ultraviolet finiteness of N=8 supergravity. Remember all those claims made for string theory that it is the only way to tame the short-distance fluctuations of a quantum theory of gravity?

Update: One of the authors of the four-loop paper wrote to me with some comments about it, which he gave me permission to post here:

I just wanted to point out what I see as two of the interesting things with this calculation:

1) Honest four-loop QFT calculations in (massless) gauge and gravity theories are now possible, if not exactly trivial. This isn’t just “big fancy computers.” Sure, computers help with the book-keeping of the calculation, but no computer in the world could have accomplished this by naively marching through Feynman diagrams (just look at the size of the expression of 3-graviton Feynman rule in your favorite gauge, and do vertex counting on the number of distinct graph topologies). Rather, this is due to advances in understanding how to manipulate lower-loop and tree-level scattering amplitudes to get (complete) higher-loop scattering amplitudes.

To understand how powerful this is, consider the following: the construction of the four-loop four-point N=4 super-Yang-Mills amplitude required (as input) nothing more complicated than the Parke-Taylor expressions for MHV three-, four-, and five-gluon scattering amplitudes in four dimensions — not even requiring the (very nice) recursion relations for higher point trees mentioned in the IAS piece above. (Verification, of course, required more 🙂 ). If you’ve seen the Parke-Taylor expressions you’ll know how simple they are! The construction and verification of the four-loop N=8 supergravity amplitude requires only knowing the four-loop four-point N=4 super-Yang-Mills amplitude.

Even had we not gotten the nice result regarding the tame UV behavior, getting to the point where these types of calculations are doable is I think important in its own right, and possibly even more important in the long-run. I should probably point out that these types of approaches can and are being generalized to more physical theories, like the exciting high-multiplicity one-loop QCD work going on.

2) Maybe there’s a perturbatively finite (point-like) QFT of gravity in 4D. This is exciting as it suggests that QFT could be a more powerful framework for describing the universe than people have been giving it credit for recently. We do believe that, if it is perturbatively finite, it will be so due to some previously unrecognized symmetry or dynamical mechanism that once understood should greatly improve our understanding of gravity. There does seem to be some connection with the very good scaling behavior of tree-level pure-graviton amplitudes in theories related to Einstein-Hilbert gravity.

That being said, we really don’t have anything to say about its non-perturbative behavior. Really. Nothing at all. It absolutely could require non-perturbative completeness from string theory. It could already be non-perturbatively complete in a way that’s best described by a string theory in certain regimes (emergent string theory if you like). Maybe it only works with higher-dimensional invisi-pink elephants. I really don’t know; it’s not what we’re after right now. I certainly encourage people to consider working on non-perturbative N=8 questions if they’re curious!

Not to be overly contrarian, but I wouldn’t characterize any of this as a blow against string theory, and I don’t think most string theorists see it as such. String theorists have, on the whole, been very supportive of this line of research (even if it might mean a small technical modification of certain sentences in the introduction of certain texts 🙂 ). Besides one of our collaborators (Radu) also being a practicing string-theorist, we’ve met with a lot of support from all sorts of people who appreciate calculation, and are honestly curious about the results. Besides, there have been very strong string-theorists actively working on understanding this from the string-side. In terms of community support, i.e. not just good individuals here and there, Zvi’s been invited to talk at Strings ’09, Lance talked at ’08, and I think Zvi talked at ’07 if I remember correctly.

I, of course, can’t help but flinch a little when people glibly say string theory is the only way to talk about gravity (which is manifestly wrong, e.g. the CFT side of the AdS/CFT *duality*). Most thoughtful string-theorists I’ve met who say something similar, however, are using it as a shorthand for a much more long-winded statement which is accurate. Namely they’re compressing a statement regarding the level of understanding we’ve gained about gravity and gauge theories and non-perturbative solutions through string-theoretic analysis, which we haven’t from anywhere else. As we can see by my comment here, there are perils to giving in to long-windiness, so I tend to refrain from giving them too hard a time about it. There is trouble of course when similar statements are mindlessly parroted by the thoughtless, but the thoughtless tend to generate grief generically in any case.

John Joseph M. Carrasco
http://www.physics.ucla.edu./~jjmc/

I’m afraid that most of you have already missed one event here in New York involving someone who blogs about high energy physics. This was Tommaso Dorigo’s visit this Sunday to New York for a few hours. Luckily for you, he blogs about it, with pictures, here. I’m quite pleased to have finally gotten a chance to meet him in person. My mother feels the same way.

There is something else though here in New York, next Monday, that you still haven’t missed. I’ll be talking and answering questions at an event organized by the Center for Inquiry, which will take place at the Brooklyn Society for Ethical Culture in Park Slope. More information about the event is available here.