String or M-theory in the background of Kerr-AdS black holes is thought to
be dual to the large N limit of certain conformal field theories on a rotat
ing sphere at finite temperature. The five dimensional black hole is associ
ated to N = 4 supersymmetric Yang-Mills theory on a rotating three-sphere a
nd the four dimensional one to the superconformal field theory of coincidin
g M2 branes on a rotating two-sphere. The thermodynamic potentials can be e
xpanded in inverse powers of the radius of the sphere. We compute the leadi
ng and subleading terms of this expansion in the field theory at one loop a
nd compare them to the corresponding supergravity expressions. The ratios b
etween these terms at weak and strong coupling turn out not to depend on th
e rotation parameters in the case of N = 4 SYM. For the field theory living
on one M2 brane we find a subleading logarithmic term. No such term arises
from the supergravity calculation.