  It has been conjectured that a near-extreme Kerr black hole is described by a
2d CFT. Previous work has shown that CFT operators dual to axisymmetric
gravitational perturbations have integer conformal weights. In this paper, we
study the analogous problem in 5d. We consider the most general near-extreme
vacuum black hole with two rotational symmetries. This includes Myers-Perry
black holes, black rings and Kaluza-Klein black holes. We find that operators
dual to gravitational (or electromagnetic or massless scalar field)
perturbations preserving both rotational symmetries have integer conformal
weights, the same for all black holes considered.
