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

TL;DR

This paper investigates the large N phase transition in q-deformed Yang-Mills theory on the sphere, connecting topological strings, black hole entropy, and matrix models, and analyzing the chiral string expansion and phase structure.

Contribution

It provides a detailed analysis of the chiral theory, constructs a matrix model with three phases, and links the phase transition to divergences in topological string perturbation series.

Findings

Identification of three phases in the matrix model.

Explicit comparison confirming the topological string expansion.

Critical point corresponds to divergence in string perturbation series.

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.