Black hole entropy, marginal stability and mirror symmetry

We consider the superconformal quantum mechanics associated to BPS black holes in type II B Calabi-Yau compactifications. This quantum mechanics describes the dynamics of D-branes in the near-horizon attract or geometry of the black hole. In many cases,the black hole entropy can be found by counting the number of chiral primaries in this quantum mechanics. Both the attract or mechanism and notions of marginal stability play important roles in generating the large number of micro states required to explain this entropy. We compute the microscopic entropy explicitly in a few different cases, where the theory reduces to quantum mechanics on the moduli space of special Lagrangians. Under certain assumptions, the problem may be solved by implementing mirror symmetry as three T-dualities: this is essentially the mirror of a calculation by Gaiotto, Strominger and Yin. In some simple cases, the calculation may be done in greater generality without resorting to conjectures about mirror symmetry. For example, the K3 x T-2 case may be studied precisely using the Fourier-Mukai transform.