Wednesday, May 03, 2006

Ari Pakman and Rajesh Gopakumar

Ari

Ari Pakman et al. have done something that should have been calculated eight years ago or so: they have verified the three-point functions of the chiral primary operators in the AdS3/CFT2 correspondence. Recall that the same task in AdS5/CFT4 was solved by Lee, Minwalla, Rangamani, and Seiberg in 1998.

The calculation of Ari and his company starts with the Wess-Zumino-Witten models for the groups SU(2) and SL(2,R) that are combined in various ways. The intermediate results depend on the double gamma function and similar monsters. But all these complicated functions eventually cancel between the SU(2) and SL(2,R) parts of the theory to give you a very simple result (essentially equal to one) - one that matches the correlators in the symmetric orbifold CFTs that describe the boundary conformal field theory - correlators calculated by Lunin and Mathur, among others. I can't tell you more details because the paper by Ari et al. is yet to be published.

When Ari visited Harvard at the end of 2004, he showed a picture of Che Guevara on one of his transparencies. At that time, I did not know that particular communist bastard, so I asked Ari who was that - and Ari answered that it was a Czech dissident. Ari assumed that I was joking - because we certainly had to hear about Che all the time, he thought - but I was not joking and in fact the Czechoslovak communists did not tell us a single nice word about Che. He was never popular in Czechoslovakia and as far as I can tell, the Czechoslovak communists did not trust allies such as Che.

Rajesh

Rajesh Gopakumar is continuing with his program to derive the worldsheet theory of a string from the known gauge theory on the boundary of the AdS spacetime. He has a sophisticated sequence of steps to translate the diagrams in gauge theory - and he considers free diagrams in the free gauge theory only. By imagining that the worldsheet is discretized in a particular way, he can construct the hypothetical worldsheet correlators that indeed lead, after an integral over the worldsheet positions (and perhaps other moduli, if you considered string loops), to the simple power-law correlators of the chiral primaries on the CFT side.

The worldsheet correlators satisfy all the usual properties that you expect from a CFT, and as Davide Gaiotto has pointed out, they resemble powers of correlators of spin fields in the Ising model. Indeed, it is not unnatural to expect that the vertex operators for physical states in the hypothetical CFT are represented by some kind of spin fields.