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

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

2004-10-12

arxiv.org/abs/hep-th/0410141v2

JHEP0411:007,2004

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/1126-6708/2004/11/007

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.

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