  We show that generic supersymmetric AdS_5 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 formulae.
