Another day, another cup of soup and a sandwich for lunch. Today it was ham soup and a pineapple sandwich (my Dutch and my taste buds are not good enough to understand what the other ingredients were).
This morning we had a review lecture on the pure spinor formalism by Nathan Berkovits. If you want to learn this formalism, why not start with the reviews here (and here [or the blog article here]) and then end with the paper here. If you do this in one-and-a-half hours, but ensure you explain it to yourself very clearly, you will have your own simulation of this morning's nice review. Or, if you are feeling little tired, you could watch the video of Yaron Oz's lectures to the CERN winter school.
Following Berkovits, Andreas Gustavsson, the third man of the present Bagger-Lambert multiple membranes revolution, spoke on..."Multiple M2's". He included his paper from last year and his more recent work on how the membrane triple product identity aids amplitude calculations. His talk was followed by thirty minutes from Frederik Denef, talking under the title of "the string landscape of quantum critical superconductors", which refers to work in progress with Sean Hartnoll. The central theme was that there are two landscapes in physics. The string theory landscape, constructed inside a unique fundamental theory (M-theory), with low energy excitations (gravitons, "3-formons" :) and superpartners) and where the intricate landscape is considered "party-spoiling". The second landscape is the condensed matter landscape, constructed from a unique theory (the standard model), with low energy excitations (neutrons, protons and electrons) and where the landscpe is still intricate but is useful. The heuristic message is that these two landscapes may be very similar. Denef gave us a toy model two dimensional array of spin one-half particles that illustrated the idea of quantum critical points - points in phase space where a second order phase transition occurs at zero temperature. The crucial features are all summed up in his graph:
A second example of criticality involved superconductors and whose features were given by a toy-modelin two dimensions: a Bose-Hubbard model. There is a phase transition between being an insulator and being a superconductor. This picture was to be compared with a charged scalar field in a Reisner-Nordstrom AdS background. The idea (due to Gubser) was that there is a quantum critical point here too that separates insulation from superconductivity. Namely when electrostatic repulsion of the charged scalar is larger than its gravitational attraction towards the singularity in the space-time, then a halo or cloud of charge forms around the black-hole. This is the superconducting picture. Otherwise the charge falls into the horizon and we have the insulating picture. We are to expect to hear more about this superconducting phase from Gary Horowitz tomorrow. Denef told us one could be optimistic that this picture could be constructed in string theory. Citing the "Gravity=Weakest force" paper of Arkani-Hamed, Motl, Nicolis and Vafa, Denef said that Reissner-Nordstrom black-holes should be able to decay and so there was an expectation that the electrostatic repulsion > gravitational attraction regime should exist. Perhaps microscopic physics and macroscopic physics are not so different after all?
In the last morning talk, Giulio Bonelli spoke under the title "On gauge/string correspondence and mirror symmetry" and you can read his preprint here. In the afternoon we heard an exuberant Vijay Balasubramanian talk about getting something from nothing. His title was "Statistical predictions from anarchic field theory landscapes". Out of chaos certain coarse-grained properties could become predictable he said, read more in the preprint. The final thirty minute talk of the day was given by Diederik Roest, who talked on my favourite subject: "The Kac-Moody algebras of supergravity". The talk covered decomposition of the algebra, the correspondence between de-forms, top forms and E(11) (preprint) and also his work with Axel Kleinschmidt on identifying the Kac-Moody algebras that are appropriate to three dimensional scalar theories with a quarter or less of the full supersymmetry (preprint). After coffee, we had a gong show for some researchers but unfortunately we had no gong. Poor Pierre Vanhove must have been kicking himself that he hadn't packed his legendary cowbell...
On my walk back home I encountered two mathematical omens in odd places, first a van that seemed like it could go to infinity and beyond:
And, second, I saw the hotel I should have been staying at:
Unfortunately there were no giraffes helping zebras to escape the circus... despite this bizarre story I'm not sure that truth is stranger than fiction. In fiction the same story could have happened but the giraffe might have been smoking a cuban cigar and saying that he loved it when a plan came together and all the while Pierre Vanhove skipping in front leading the animals with the merry din of his cowbell.
Math and Physics Summer Camps
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