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Branes, black holes and topological strings on toric Calabi-Yau manifolds. (English) Zbl 1226.81249

Summary: We develop means of computing exact degeneracies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D \(q\)-deformed Yang-Mills theory on necklaces of \(\mathbb{P}^{1}\)’s. As explicit examples we consider local \(\mathbb{P}^{2}, \mathbb{P}^{1} \times \mathbb{P}^{1}\) and \(A_{k}\) type ALE space times \(\mathbb{C}\). At large \(N\) the D-brane partition function factorizes as a sum over squares of chiral blocks, the leading one of which is the topological closed string amplitude on the Calabi-Yau. This is in complete agreement with the recent conjecture of Ooguri, Strominger and Vafa.

MSC:

81T45 Topological field theories in quantum mechanics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83C57 Black holes
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References:

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