One of the things that he clarified for me was the origin of the AdS/CFT derivation of the lower bound for the viscosity that we discussed for example here. In a huge class of theories, the viscosity must be greater than "1/4.pi" times the entropy density, counted in fundamental units. It seems to be true in general. In a subclass of the theories, one may construct a gravitational dual of the theory. How do you derive the bound from the gravitational dual? Let's start in the field theory. The viscosity may be calculated, in the field theory, from some two-point function of the stress-energy tensor. This quantity is directly translated to the gravitational picture.
The relevant calculation involves a graviton propagator in the background of a large (greater than the AdS curvature radius) AdS Schwarzschild black hole; such a black hole is generically dual to the lowest-viscosity environment. It's a rather tedious calculation but you may get the result including the numerical pre-factor. A simpler calculation - one that Andreas found less comprehensible - involves the quasinormal modes. But Andrei Starinets comments:
Viscosities (shear and bulk) of thermal theories with gravity duals can be computed basically in three ways (all inter-related, of course):
- via Green-Kubo formulae (graviton's absorption on the gravity side)
- by computing the (retarded) correlator of stress-energy tensor in (Lorentzian signature) AdS/CFT
- by computing the lowest quasinormal frequency of the relevant gravitational background. This frequency is precisely the hydrodynamic pole in the above mentioned correlator. Computing quasinormal frequencies is sometimes technically easier than computing full correlators, but it is absolutely rigorous. If you like, please look through our recent paper with Pasha Kovtun, hep-th/0506184, where we sort of summarize this.
