Central charge of supersymmetric 5D anti-de sitter space solutions of type IIB supergravity.

We show that generic supersymmetric 5D anti-de Sitter solutions of type IIB supergravity admit a canonical contact structure. This structure determines the central charge of the dual field theory and the conformal dimension of operators dual to supersymmetric wrapped D3-branes. Hence both quantities can be calculated using incomplete information about the solutions, allowing us to prove that they are rational numbers for solutions with a U(1) R symmetry, in agreement with field theory expectations. We also discuss related Duistermaat-Heckman integrals and localization formulas.