A Comment on Quantum Distribution Functions and the OSV Conjecture

Abstract

Using the attractor mechanism and the relation between the quantization of $H^3(M)$ and topological strings on a Calabi Yau threefold $M$ we define a map from BPS black holes into coherent states. This map allows us to represent the Bekenstein-Hawking-Wald entropy as a quantum distribution function on the phase space $H^3(M)$. This distribution function is a mixed Husimi/anti-Husimi distribution corresponding to the different normal ordering prescriptions for the string coupling and deviations of the complex structure moduli. From the integral representation of this distribution function in terms of the Wigner distribution we recover the Ooguri-Strominger-Vafa (OSV) conjecture in the region "at infinity" of the complex structure moduli space. The physical meaning of the OSV corrections are briefly discussed in this limit.

27 pages. v2:reference and footnote added

References in corpus (7)

• A Farey Tail for Attractor Black Holes
• Two Dimensional Yang-Mills, Black Holes and Topological Strings
• Attractors and the Holomorphic Anomaly
• From AdS3/CFT2 to Black Holes/Topological Strings
• BPS Microstates and the Open Topological String Wave Function
• Topological Strings and (Almost) Modular Forms
• Crystals and intersecting branes

Cited by in corpus (4)

• N=2 Supersymmetric Black Attractors in Six and Seven Dimensions
• A Classical Bound on Quantum Entropy
• Black Holes in Type IIA String on Calabi-Yau Threefolds with Affine ADE Geometries and q-Deformed 2d Quiver Gauge Theories
• Geometric Transition as a Change of Polarization