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

Abstract

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.

49 pages, 9 figures

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• A Note on Knot Invariants and q-Deformed 2d Yang-Mills
• Localization for Wilson Loops in Chern-Simons Theory
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• Unitary Chern-Simons matrix model and the Villain lattice action
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• Universal Character and Large N Factorization in Topological Gauge/String Theory
• Calabi-Yau Orbifolds and Torus Coverings
• Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
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• Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras
• New Phase Transitions in Chern-Simons Matter Theory
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• String Duals of Two-Dimensional Yang-Mills and Symmetric Product Orbifolds
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• Enumerative geometry of surfaces and topological strings