Configurations of N probe D0-branes in a Calabi-Yau black hole are studied. A large degeneracy of near-horizon bound states are found which can be described as lowest Landau levels tiling the horizon of the black hole. These states preserve some of the enhanced supersymmetry of the near-horizon AdS 2 × S 2 × CY 3 attractor geometry, but not of the full asymptotically flat solution. Supersymmetric non-abelian configurations are constructed which, via the Myers effect, develop charges associated with higher-dimensional branes wrapping CY 3 cycles. An SU (1, 1|2) superconformal quantum mechanics describing D0-branes in the attractor geometry is explicitly constructed.

The problem of finding supersymmetric brane configurations in the near-horizon attractor geometry of a Calabi-Yau black hole with magnetic-electric charges (p I , q I ) is considered. Half-BPS configurations, which are static for some choice of global AdS 2 coordinate, are found for wrapped brane configurations with essentially any four-dimensional charges (u I , v I ). Half-BPS multibrane configurations can also be found for any collection of wrapped branes provided they all have the same sign for the symplectic inner product p I v I − u I q I of their charges with the black hole charges. This contrasts with the Minkowski problem for which a mutually preserved supersymmetry requires alignment of all the charge vectors. The radial position of the branes in global AdS 2 is determined by the phase of their central charge.

We consider the superconformal quantum mechanics associated to BPS black holes in type IIB Calabi-Yau compactifications. This quantum mechanics describes the dynamics of Dbranes in the near-horizon attractor 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 attractor mechanism and notions of marginal stability play important roles in generating the large number of microstates 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 × T 2 case may be studied precisely using the Fourier-Mukai transform.

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