A Matrix Model for Random Surfaces with Dynamical Holes

TL;DR

This paper introduces a matrix model for random surfaces with dynamical holes, analyzing its phases and confirming universality with previous models, while identifying a new phase boundary with distinct singular behaviour.

Contribution

It presents a novel matrix model for oriented loops on random surfaces, extending previous models and analyzing its critical phases and singular behaviours.

Findings

Two critical phases with Kazakov's model behaviour

Confirmation of universality in the continuum limit

Identification of a new phase boundary with unique singularity

Abstract

A matrix model to describe dynamical loops on random planar graphs is analyzed. It has similarities with a model studied by Kazakov, few years ago, and the O(n) model by Kostov and collaborators. The main difference is that all loops are coherently oriented and empty. The free energy is analytically evaluated and the two critical phases are analyzed, where the free energy exhibits the same critical behaviour of Kazakov's model, thus confirming the universality of the description in the continuum limit (surface with small holes, and the tearing phase). A third phase occurs on the boundary separating the above phase regions, and is characterized by a different singular behaviour, presumably due to the orientation of loops.