From AdS3/CFT2 to black holes/topological strings

The elliptic genus Z(BH) of a large class of 4D black holes can be expressed as an M-theory partition function on an AdS(3) x S-2 x CY3 attractor. We approximate this partition function by summing over multiparticle chiral primary states of membranes which wrap curves in the CY3 and tile Landau levels on the horizon S-2. Significantly, membranes and antimembranes can preserve the same super charges if they occupy antipodal points on the horizon. It is shown the membrane contribution to Z(BH) gives precisely the topological string partition function Z(top) while the antimembranes give (Z) over bar (top), implying Z(BH) = vertical bar Z(top)vertical bar(2) in this approximation.