  AdS/CFT predicts a precise relation between the central charge a, the scaling
dimensions of some operators in the CFT on D3-branes at conical singularities
and the volumes of the horizon and of certain cycles in the supergravity dual.
We review how a quantitative check of this relation can be performed for all
toric singularities. In addition to the results presented in hep-th/0506232, we
also discuss the relation with the recently discovered map between toric
singularities and tilings; in particular, we discuss how to find the precise
distribution of R-charges in the quiver gauge theory using dimers technology.
