Complex saddles in the Gross-Witten-Wadia matrix model

Abstract

We give an exhaustive characterization of the complex saddle point configurations of the Gross-Witten-Wadia matrix model in the large-N limit. In particular, we characterize the cases in which the saddles accumulate in one, two, or three arcs, in terms of the values of the coupling constant and of the fraction of the total unit density that is supported in one of the arcs, and derive an explicit condition for gap closing associated to nonvacuum saddles. By applying the idea of large-N instanton we also give direct analytic derivations of the weak-coupling and strong-coupling instanton actions.

References in corpus (3)

• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• A Study of U(N) Lattice Gauge Theory in 2-dimensions
• Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence

Cited by in corpus (4)

• Wilson loops in unitary matrix models at finite $N$
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• Large $N$ expansion of Wilson loops in the Gross-Witten-Wadia matrix model
• Phase space and phase transitions in the Penner matrix model with negative coupling constant