Flows for rectangular matrix models

TL;DR

This paper investigates the multicritical behavior of rectangular matrix models, deriving free energy, string equations, and flow equations, and explores the almost-square matrix limit as a realization of open-closed string theory scaling equations.

Contribution

It provides new analytical results on the multicritical behavior and scaling limits of rectangular matrix models, connecting them to string theory frameworks.

Findings

Free energy calculated via saddle point approximation.

At the triple-scaling point, results match recursion formulae.

Almost-square matrix limit models open-closed string theory scaling equations.

Abstract

Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulae. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric solutions are also examined for the limit of almost-square matrix models. This limit is shown to provide an explicit matrix model realization of the scaling equations proposed to describe open-closed string theory.