Interaction of boundaries with heterogeneous matter states in matrix models

TL;DR

This paper investigates boundary interactions with heterogeneous matter states in matrix models, revealing geometric interpretations and deriving equations that determine disk amplitudes, enhancing understanding of boundary matter interactions.

Contribution

It introduces analysis of non-homogeneous boundary conditions in matrix models and derives Schwinger-Dyson equations for disk amplitudes with complex boundary matter configurations.

Findings

Relations between matter degrees of freedom in two- and three-matrix models

Geometric interpretation of boundary interactions involving different matter states

Derivation of Schwinger-Dyson equations for disk amplitudes

Abstract

We study disk amplitudes whose boundary conditions on matter configurations are not restricted to homogeneous ones. They are examined in the two-matrix model as well as in the three-matrix model for the case of the tricritical Ising model. Comparing these amplitudes, we demonstrate relations between degrees of freedom of matter states in the two models. We also show that they have a simple geometrical interpretation in terms of interactions of the boundaries. It plays an important role that two parts of a boundary with different matter states stick each other. We also find two closed sets of Schwinger-Dyson equations which determine disk amplitudes in the three-matrix model.