Retarded Green's Function from Rotating AdS Black Holes: Emergent CFT2 and Viscosity
Abstract
Using the AdS/CFT correspondence we consider the retarded Green's function in the background of rotating near-extremal AdS4 black holes. Following the canonical AdS/CFT dictionary into the asymptotic boundary we get a CFT3 result. We also take a new route and zoom in on the near-horizon region, blow up this region and show that it yields a CFT2 result. We argue that the decoupling of the near-horizon region is akin to the decoupling of the near-throat region of a D3-brane, which led to the original formulation of the AdS/CFT correspondence, thus implying that the Kerr/CFT correspondence follows as a decoupling of the standard AdS/CFT correspondence applied to rotating black holes. As a byproduct, we compute the shear viscosity to entropy density ratio for the strongly coupled boundary CFT3, and find that it violates the 1 / (4 π) bound.