Black-holes, topological strings and large N phase transitions

Details Black-holes, topological strings and large N phase transitions Black-holes, topological strings and large N phase transitions

2005-12-17

arxiv.org/abs/hep-th/0512213v1

J.Phys.Conf.Ser.33:13-25,2006

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, 3 figures; Invited talk given at QG05, Cala Gonone (Italy), September 2005

Scientific paper

The counting of microstates of BPS black-holes on local Calabi-Yau of the form ${\mathcal O}(p-2)\oplus{\mathcal O}(-p) \longrightarrow S^2$ is explored by computing the partition function of q-deformed Yang-Mills theory on $S^2$. We obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces to the trivial sector and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point, instantons are enhanced and the theory undergoes a phase transition into a strong coupling regime. The transition from the strong coupling phase to the weak coupling phase is of third order.

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