One- and two-matrix models and random cylindre with two-coloured boundaries

TL;DR

This paper explores one- and two-matrix models as tools for studying conformal field theories with boundaries, introducing a new method to calculate the generating function of two-colored boundary cylinders.

Contribution

It presents a novel calculation of the generating function for random cylinders with two-colored boundaries using the loop equations method.

Findings

Derived the generating function for two-colored boundary cylinders

Linked matrix models with conformal field theories and random surfaces

Introduced a new computational approach for boundary-related quantities

Abstract

In this training course report, I briefly present the one- and two-matrix models as tools for the study of conformal field theories with boundaries. In a first part, after a short historical presentation of random matrices, I present the matrix models' formalism, their diagramatic interpretation, their link with random surfaces and conformal field theories and the "loop equations" method for the 2-matrix model. In a second part, I use this method for the calculation of the generating function of random cylindres whose boundaries are two-coloured, which was not know before.