We derive a geometric formulation of the 2d central charge cr from
infinite families of 4d N=1 superconformal field theories
topologically twisted on constant curvature Riemann surfaces. They correspond
to toric quiver gauge theories and are associated to D3 branes probing five
dimensional Sasaki-Einstein geometries in the AdS/CFT correspondence. We show
that cr can be expressed in terms of the areas of the toric diagram
describing the moduli space of the 4d theory, both for toric geometries with
smooth and singular horizons. We also study the relation between a-maximization
in 4d and c-extremization in 2d, giving further evidences of the mixing of the
baryonic symmetries with the exact R-current in two dimensions.Comment: 39 pages, 21 figures, minor change