Most of the lectures from this year’s Jerusalem Winter School in Theoretical Physics are now available online. David Gross was the main organizer, and the choice of topics reflects his point of view on what is interesting these days in theoretical physics. The landscape and anthropics were pretty much completely suppressed (although Michael Dine did manage to slip in a mention, his slides are here). The idea of “string phenomenology”, i.e. getting the standard model out of a unified string theory and saying something about particle physics has fallen by the way-side.
In his summary talk (given at the beginning of the conference), Gross described the same point of view he has promoted for many years now. He thinks something is missing in our understanding of string theory (“we don’t know what string theory is”) which will somehow fix the failure of ideas about string theory unification. This failure though doesn’t matter anyway, since he now claims that string theory = QFT, based on gauge-gravity duality, and thus “string theory cannot be killed”. It’s very unclear how this equivalence claim fits together with the “we don’t know what string theory is” claim, since we do know what QFT is (we have a very good understanding of the Standard Model). It seems that Gross would like to define away much of the troubles surrounding string theory.
One idea that Gross has favored for a very long time is that string theory is telling us that we must give up our usual notions of space and time, only recovering them in some limit. Two of the series of lectures at the school were about rather grandiose attempts to do something along these lines. There were three lectures by Erik Verlinde on his ideas about “emergent gravity”. I continue to not be able to make much sense of this program. He invokes the reasonable idea that gravity is an effective long-distance force due to unknown fundamental degrees of freedom, which may very well be true. But he doesn’t seem to have anything specific to say about the fundamental degrees of freedom strong enough to get anything new out of this. There were some ideas at the end about dark matter and dark energy, but it was unclear to me whether these go anywhere.
Much more interesting was Nima Arkani-Hamed’s series of lectures on Scattering Amplitudes and the Positive Grassmannian, which he said could have been titled “How you get spacetime from the permutation group”. The first lecture started with a philosophical introduction that he said he would limit to 5 minutes, but which went on for 40. Only the first two lectures are now online.
Unlike Verlinde’s ideas, here there are very specific calculations involved. The starting point is recent progress in understanding perturbative amplitudes for N=4 SYM (and for more general gauge theories). These involve working in twistor space, and more generally working with variables such that locality and unitarity are no longer manifest. The basic mathematics and geometrical principles at work are quite different than the standard formulation of gauge theories in terms of local variables and gauge symmetry. As usual, Arkani-Hamed makes wildly enthusiastic claims. In this case, he claims to have finally found a remarkable new understanding of the subject, based on some combinatorial objects and dramatic new mathematical ideas. He does note that this still hasn’t been written up, and that it’s the third time in the past year that he has thought he had things understood, with the last two times not working out.
I’m quite curious to see where this all goes, although I confess that I’m planning on waiting a while to try and follow the details, since this is clearly very complicated work in progress, and a 4th or 5th iteration of the fundamentals may very well be on its way over the next few months. Arkani-Hamed is talking to mathematicians, including his colleague Pierre Deligne at the IAS, and says that he is moving from the old-style of Atiyah mathematics to a new-style of Grothendieck-based mathematics. I’m not sure what this means, but suspect that Atiyah’s ideas are still in there (Grassmanians, twistors and toric varieties are subjects he has been very much involved with), and that the Grothendieck business may be an artifact of talking to Deligne, who comes from that tradition. Grothendieck was the master of generality, so his ideas can be applied to a very large fraction of mathematics.
Also lecturing on amplitudes, from a much more down-to-earth point of view, was Zvi Bern. For more from both Bern and Arkani-Hamed, see the program of the recent Amplitudes 2011 conference in Michigan. Slides from Arkani-Hamed’s talk give a better idea of what he is up to, and Bern’s slides contain his summary comments about the state of the subject. He emphasizes the connections between amplitude calculations and other fields and seems to be arguing for more attention to practical results, less to “symmetry, beauty and aesthetics”. He worries that while “Today our field is one of the hottest ones around”, the long-term future is less clear: “Is our field just another (albeit long lasting) fad?”, so attention to results relevant to the rest of physics is important for long-term health.