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Why Z_{BH} = |Z_{top}|^2
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It is argued, using an M-theory lift, that the IIA partition function on a euclidean AdS_2 x S^2 x CY_3 attractor geometry computes the modified elliptic genus Z_BH of the associated black hole in a large charge expansion. The partition function is then evaluated using the Green-Schwarz formalism. After localizing the worldsheet path integral with the addition of an exact term, contributions arise only from the center of AdS_2 and the north and south poles of S^2. These are the toplogical and anti-topological string partition functions Z_top and {\bar Z_top} respectively. We thereby directly reproduce the perturbative relation Z_BH = |Z_top|^2.
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Towards OSV in AdS
Derives Z_{S^1×S^2} ∼ |Z_{S^3_b}|^2 for 3d N=2 SCFTs and links it holographically to supersymmetric AdS4 black hole partition functions, akin to OSV.
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