INTERACTION OF BOUNDARIES WITH HETEROGENEOUS MATTER STATES IN MATRIX MODELS

We study disk amplitudes whose boundary conditions on matter configura tions 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 demonstra te relations between degrees of freedom of matter states in the two mo dels, 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 to ea ch other. We also find two closed sets of Schwinger-Dyson equations wh ich determine disk amplitudes in the three-matrix model. (C) 1998 Else vier Science B.V.