Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory

Details Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory

2005-11-03

arxiv.org/abs/hep-th/0511043v1

JHEP 0601:036,2006

Physics

High Energy Physics

High Energy Physics - Theory

49 pages, 9 figures

Scientific paper

10.1088/1126-6708/2006/01/036

We continue our study of the large N phase transition in q-deformed Yang-Mills theory on the sphere and its role in connecting topological strings to black hole entropy. We study in detail the chiral theory defined in terms of uncoupled single U(N) representations at large N and write down the resulting partition function by means of the topological vertex. The emergent toric geometry has three Kaehler parameters, one of which corresponds to the expected fibration over the sphere. By taking a suitable double-scaling limit we recover the chiral Gross-Taylor string expansion. To analyse the phase transition we construct a matrix model which describes the chiral gauge theory. It has three distinct phases, one of which should be described by the closed topological string expansion. We verify this expectation by explicit comparison between the matrix model and the chiral topological string free energies. We also show that the critical point in the pertinent phase of the matrix model corresponds to a divergence of the topological string perturbation series.

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