Complex saddles in the Gross-Witten-Wadia matrix model

TL;DR

This paper thoroughly analyzes complex saddle points in the Gross-Witten-Wadia matrix model at large N, identifying conditions for different saddle configurations and deriving instanton actions for weak and strong coupling regimes.

Contribution

It provides a comprehensive characterization of complex saddles, including conditions for gap closing and explicit derivations of instanton actions in the matrix model.

Findings

Saddles can accumulate in one, two, or three arcs depending on parameters.

Explicit conditions for gap closing in nonvacuum saddles.

Analytic derivations of instanton actions at different coupling regimes.

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.