Retarded Green's Function from Rotating AdS Black Holes: Emergent CFT${}_2$ and Viscosity

Abstract

Using the AdS/CFT correspondence we consider the retarded Green's function in the background of rotating near-extremal AdS${}_4$ black holes. Following the canonical AdS/CFT dictionary into the asymptotic boundary we get a CFT${}_3$ 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 CFT${}_2$ 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 CFT${}_3$, and find that it violates the $1/(4\pi )$ bound.

Comments: 9 pages, 4 figures; V2: 2 figures and more discussions added, published version in PRD