Macroscopic loop amplitudes in the multi-cut two-matrix models

TL;DR

This paper investigates multi-cut critical points and macroscopic loop amplitudes in two-matrix models, extending existing methods to find new solutions characterized by Jacobi polynomials in symmetric backgrounds.

Contribution

It introduces an extension of the prescription for multi-cut two-matrix models, identifying critical points and deriving new amplitude solutions using Jacobi polynomials.

Findings

Identification of critical points and potentials in multi-cut models

Derivation of new solutions for loop amplitudes in symmetric backgrounds

Use of Jacobi polynomials to realize these solutions

Abstract

Multi-cut critical points and their macroscopic loop amplitudes are studied in the multi-cut two-matrix models, based on an extension of the prescription developed by Daul, Kazakov and Kostov. After identifying possible critical points and potentials in the multi-cut matrix models, we calculate the macroscopic loop amplitudes in the Z_k symmetric background. With a natural large N ansatz for the matrix Lax operators, a sequence of new solutions for the amplitudes in the Z_k symmetric k-cut two-matrix models are obtained, which are realized by the Jacobi polynomials.