Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds

Abstract

We study the relation between c=1 matrix models at self-dual radii and topological strings on non-compact Calabi-Yau manifolds. In particular the special case of the deformed matrix model is investigated in detail. Using recent results on the equivalence of the partition function of topological strings and that of four dimensional BPS black holes, we are able to calculate the entropy of the black holes, using matrix models. In particular, we show how to deal with the divergences that arise as a result of the non-compactness of the Calabi-Yau. The main result is that the entropy of the black hole at zero temperature coincides with the canonical free energy of the matrix model, up to a proportionality constant given by the self-dual temperature of the matrix model.

arXiv comment42 pages, 10 figures. v2: Minor corrections and clarifications added. References added

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Cited by in corpus (15)

• Attractors and the Holomorphic Anomaly
• A mini-course on topological strings
• Exact 2-point function in Hermitian matrix model
• Stability of flux vacua in the presence of charged black holes
• c < 1 String from Two Dimensional Black Holes
• Type 0A matrix model of black hole, integrability and holography
• Special geometry of local Calabi-Yau manifolds and superpotentials from holomorphic matrix models
• Matrix Model and Time-like Linear Dilaton Matter
• On Type II Strings in Two Dimensions
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Topological B-model and $\hat{c}=1$ String Theory
• 4D black holes and holomorphic factorization of the 0A matrix model
• The stringy nature of the 2d type-0A black hole
• Supersymmetric Gauge Theories from String Theory
• Noncritical-Topological Correspondence: Disc Amplitudes and Noncompact Branes