Flows and Solitary Waves in Unitary Matrix Models with Logarithmic Potentials

TL;DR

This paper explores the dynamics of unitary matrix models with logarithmic potentials, revealing solitary wave solutions in the flow equations and analyzing their relation to quark flavors and nonperturbative effects.

Contribution

It derives a flow equation for the specific heat in matrix models and demonstrates the existence of solitary wave solutions linked to quark flavor number.

Findings

Flow equations exhibit a finite number of solitary waves.

Number of solitary waves likely equals the number of quark flavors.

Flow behavior diverges from two-dimensional gravity as flavor number increases.

Abstract

We investigate unitary one-matrix models coupled to bosonic quarks. We derive a flow equation for the square-root of the specific heat as a function of the renormalized quark mass. We show numerically that the flows have a finite number of solitary waves, and we postulate that their number equals the number of quark flavors. We also study the nonperturbative behavior of this theory and show that as the number of flavors diverges, the flow does not reach two-dimensional gravity.