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

TL;DR

This paper explores the holographic duals of rotating AdS black holes, revealing emergent two-dimensional CFT behavior near the horizon and showing that shear viscosity can violate the universal bound.

Contribution

It demonstrates a new near-horizon approach that yields a CFT$_2$ description and connects Kerr/CFT to the standard AdS/CFT framework for rotating black holes.

Findings

Near-horizon region yields a CFT$_2$ result

Shear viscosity to entropy density ratio violates the $1/4 ext{pi}$ bound

Decoupling of near-horizon region links Kerr/CFT to AdS/CFT

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.