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We investigate the quasinormal modes for gravitational perturbations of rotating black holes in four-dimensional anti-de Sitter (AdS) spacetime. The study of the quasinormal frequencies related to these modes is relevant to the AdS/CFT correspondence. Although results have been obtained for Schwarzschild and Reissner-Nordstrom AdS black holes, quasinormal frequencies of Kerr-AdS black holes are computed for the first time. We solve the Teukolsky equations in AdS spacetime, providing a second-order and a Padé approximation for the angular eigenvalues associated with the Teukolsky angular equation. The transformation theory and the Regge-Wheeler-Zerilli equations for Kerr-AdS are obtained.

The fermion representations and boundary conditions in five-dimensional anti-de-Sitter space are described in detail. In each case the one loop effective action is calculated for massless fermions. The possibility of topological or Wilson loop symmetry breaking is discussed.