Why Z_{BH} = |Z_{top}|^2 Academic Article uri icon

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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.


  • Beasley, Chris
  • Gaiotto, Davide
  • Guica, Monica
  • Huang, Lisa
  • Strominger, Andrew
  • Yin, Xi