We study N =4 super Yang-Mills theories on a three sphere with two kinds of chemical potentials. One is associated with the R-symmetry and the other with the rotational symmetry of S^3 (SO(4) symmetry). These correspond to the charged Kerr-AdS black
holes via AdS/CFT. The exact partition functions at zero coupling are computed and the thermodynamical properties are studied. We find a nontrivial gap between the confinement/deconfinement transition line and the boundary of the phase diagram when we include more than four chemical potentials. In the dual gravity, we find such a gap in the phase diagram to study the thermodynamics of the charged Kerr-AdS black hole. This shows that the qualitative phase structures agree between the both sides. We also find that the ratio of the thermodynamical quantities is almost well-known factor 3/4 even at the low temperature.
