Why Z_{BH} = |Z_{top}|^2

Details Why Z_{BH} = |Z_{top}|^2 Why Z_{BH} = |Z_{top}|^2

2006-08-02

arxiv.org/abs/hep-th/0608021v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, no figures

Scientific paper

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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