Black Hole Entropy, Marginal Stability and Mirror Symmetry

Abstract

We consider the superconformal quantum mechanics associated to BPS black holes in type IIB Calabi-Yau compactifications. This quantum mechanics describes the dynamics of D-branes 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 K3xT^2 case may be studied precisely using the Fourier-Mukai transform.

24 pages

References in corpus (19)

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• Dielectric-Branes
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• Supersymmetry and Attractors
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• Kahler Cone Substructure

Cited by in corpus (7)

• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• N=2 Supersymmetric Black Attractors in Six and Seven Dimensions
• Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity
• Near-horizon microstates of the D1-D5-P black hole
• Small Black Hole Constituents and Horizontal Symmetry
• Distributions of extremal black holes in Calabi-Yau compactifications
• Absorption on horizon-wrapped branes