The Relation between Mixed Boundary States in Two- and Three- Matrix Models

TL;DR

This paper explores the relationship between boundary states in two- and three-matrix models within two-dimensional quantum gravity, revealing limitations in observable spin configurations and deriving equations governing disk amplitudes.

Contribution

It establishes a connection between boundary states in different matrix models and derives a closed set of equations for disk amplitudes in the three-matrix model.

Findings

Finite insertions of different spin states are unobservable in the continuum limit

A set of eight Schwinger-Dyson equations determines disk amplitudes

Boundary state relations are characterized in two- and three-matrix models

Abstract

We discuss the relation among some disk amplitudes with non-trivial boundary conditions in two-dimensional quantum gravity. They are obtained by the two-matrix model as well as the three-matirx model for the case of the tricritical Ising model. We examine them for simple spin configurations, and find that a finite number of insertions of the different spin states cannot be observed in the continumm limit. We also find a closed set of eight Schwinger-Dyson equations which determines the disk amplitudes in the three-matrix model.