Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-11-30
Nucl.Phys.B715:304-348,2005
Physics
High Energy Physics
High Energy Physics - Theory
56 pages, 4 figures, harvmac; minor changes, references and acknowledgments added
Scientific paper
10.1016/j.nuclphysb.2005.02.035
We count the number of bound states of BPS black holes on local Calabi-Yau three-folds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a q-deformed Yang-Mills theory on the Riemann surface. Following the recent connection between the black hole entropy and the topological string partition function, we find that for a large black hole charge N, up to corrections of $O(e^{-N})$, $Z_{BH}$ is given as a sum of a square of chiral blocks, each of which corresponds to a specific D-brane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The sub-leading chiral blocks involve topological string amplitudes with D-brane insertions at 2g-2 points on the Riemann surface analogous to the $\Omega$ points in the large N 2d Yang-Mills theory. The finite N amplitude provides a non-perturbative definition of topological strings in these backgrounds. This also leads to a novel non-perturbative formulation of c=1 non-critical string at the self-dual radius.
Aganagic Mina
Ooguri Hirosi
Saulina Natalia
Vafa Cumrun
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