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 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.

supersymmetric black attractors in six and seven dimensions

“…We also have the usual globally defined complex holomorphic 3-form of the CY3 Ω (3,0) together with its antiholomorphic partner Ω (0,3) . These quantities play an important role in type IIB superstring on the mirror of the Calabi-Yau threefold [44].…”

Absorption on horizon-wrapped branes

“…(25) 5 We have F = 4π 1 2i √ gg rr`φ ∂rφ − φ∂rφ´with ds 2 = − r 2 R 2 dt 2 + R 2 r 2 dr 2 + R 2 dΩ 2 2 . The 4π comes from integration over the S 2 .…”

Near-horizon microstates of the D1-D5-P black hole

“…The mirror type IIB black hole case was considered in [8], and further related work appears in [9,10].…”

“…Under the U-duality transforming frame A into frame B, a D2-brane wrapping S 2 in frame A transforms as indicated in table 2. The first arrow is essentially mirror symmetry, and leads to the near-horizon probe picture discussed in [8]. The final probe configuration in frame B is a Kaluza-Klein (KK) monopole wrapped on the near-horizon S 3 /Z W as well as on T 2 and whose Taub-NUT direction is along S 1 .…”