The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit

TL;DR

This paper analyzes the critical points of the two-matrix model in the double scaling limit, characterizing their properties and solving related equations using advanced mathematical methods.

Contribution

It introduces a detailed characterization of the continuous series of critical points and applies conformal field theory techniques to solve the Schwinger-Dyson equations.

Findings

Critical points characterized by complex parameters and a natural number n.

Analytic critical potentials with radius of convergence depending on parameters.

Solution of Schwinger-Dyson equations using conformal field theory methods.

Abstract

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)< 0), and a natural number n (n>=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.