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Black hole entropy, marginal stability and mirror symmetry

Paul S. Aspinwall1, Alexander Maloney2 and Aaron Simons3

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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 K3 × T2 case may be studied precisely using the Fourier-Mukai transform.

Keywords

D-branes

Black Holes in String Theory

 

E-print Number: hep-th/0610033

Cited: by |

Refers: to

PACS

04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics

11.25.Mj Compactification and four-dimensional models

11.25.Hf Conformal field theory, algebraic structures

11.30.Pb Supersymmetry

11.25.Uv D branes

Subjects

Gravitation and cosmology

Particle physics and field theory

Dates

Issue 07 (July 2007)

Received 26 March 2007, accepted for publication 20 June 2007

Published 11 July 2007



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