Last friday (06/01/07), I attended the last of the Winter 2007 Caltech High Energy Seminars. The talk was at 1pm, given by KITP post-doc Sean Hartnoll. Hartnoll discussed topological phase changes of N=4 SYM theory (hep-th/0703100). Using both numerical and analytical techniques, Hartnoll found that at weak coupling, the six-sphere eigenvalue distribution transitions to a five-sphere distribution.
An interesting interpretation of this second order phase transition involves the fate of the large AdS black hole spacetime at weak coupling. Given that there are no further phase transitions as a function of coupling, the AdS black hole is described by the five-sphere eigenvalue distribution.
Hartnoll also explained how the five-sphere distribution generalizes the two-dimensional quantum Hall effect. During the question and answer session I mentioned the four and eight-dimensional quantum Hall effects to Hartnoll. He agreed that it would be interesting if his techniques could be applied in such dimensions.