From AdS3/CFT2 to black holes/topological strings

Abstract

The elliptic genus ZBH of a large class of 4D black holes can be expressed as an M-theory partition function on an AdS3 × S2 × 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 supercharges if they occupy antipodal points on the horizon. It is shown the membrane contribution to ZBH gives precisely the topological string partition function Ztop while the antimembranes give top, implying ZBH ≤ |Ztop|2 in this approximation. © SISSA 2007.