Interaction of boundaries with heterogeneous matter states in matrix models

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.

20 pages, LaTex, 2 eps figures, comments added, introduction replaced, version to appear in Nuclear Physics B

References in corpus (7)

• Rational Theories of 2D Gravity from the Two-Matrix Model
• String Field Theory of Noncritical Strings
• Combinatorial Solution of the Two-Matrix Model
• String Field Theory of $c\le 1$ Noncritical Strings
• String Field Theory in the Temporal Gauge
• Stochastic Hamiltonian for Non-Critical String Field Theories from Double-Scaled Matrix Models
• The Relation between Mixed Boundary States in Two- and Three- Matrix Models

Cited by in corpus (1)

• Geometrical Construction of Heterogeneous Loop Amplitudes in 2D Gravity