Large N and Bethe ansatz

TL;DR

This paper explores the connection between an integrable model related to the Gaudin magnet and matrix models, using Bethe ansatz and orthogonal polynomials, especially in the large N limit.

Contribution

It establishes a link between the Bethe ansatz solution of an integrable system and the matrix model's correlators in the large N limit.

Findings

Large N limit corresponds to the thermodynamic limit of the integrable system.

Bethe ansatz acts as a generating function for matrix model correlators.

The approach unifies integrable models and matrix model techniques.

Abstract

We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brezin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal polynomials and saddle point approximation. Lagre $N$ limit of the matrix model corresponds to the thermodynamic limit of the integrable system. In this limit (functional) Bethe ansatz is the same as the generating function for correlators of the matrix models.