Black hole attractors and the topological string

A simple relationship of the form ${Z}_{\mathrm{B}\mathrm{H}}=|{Z}_{\mathrm{t}\mathrm{o}\mathrm{p}}{|}^{2}$ is conjectured, where ${Z}_{\mathrm{B}\mathrm{H}}$ is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and ${Z}_{\mathrm{t}\mathrm{o}\mathrm{p}}$ is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wave function defined by the topological string partition function.