Black hole entropy, marginal stability and mirror symmetry

We consider the superconformal quantum mechanics associated to BPS blackholes in type IIB Calabi-Yau compactifications. This quantum mechanicsdescribes the dynamics of D-branes in the near-horizon attractor geometry ofthe black hole. In many cases, the black hole entropy can be found by countingthe number of chiral primaries in this quantum mechanics. Both the attractormechanism and notions of marginal stability play important roles in generatingthe large number of microstates required to explain this entropy. We computethe microscopic entropy explicitly in a few different cases, where the theoryreduces to quantum mechanics on the moduli space of special Lagrangians. Undercertain assumptions, the problem may be solved by implementing mirror symmetryas three T-dualities: this is essentially the mirror of a calculation byGaiotto, Strominger and Yin. In some simple cases, the calculation may be donein greater generality without resorting to conjectures about mirror symmetry.For example, the K3xT^2 case may be studied precisely using the Fourier-Mukaitransform.Comment: 24 page