Black Holes and Large Order Quantum Geometry
Abstract
We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations -which seem necessary to resolve the so-called entropy enigma in the OSV conjecture- do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.
Cite
@article{arxiv.0704.2440,
title = {Black Holes and Large Order Quantum Geometry},
author = {Min-xin Huang and Albrecht Klemm and Marcos Marino and Alireza Tavanfar},
journal= {arXiv preprint arXiv:0704.2440},
year = {2009}
}