A MATRIX MODEL FOR RANDOM SURFACES WITH DYNAMICAL HOLES

A matrix model to describe dynamical loops on random planar graphs is analysed. It has similarities with a model studied by Kazakov, a few y ears ago, and the O(n) model of Kostov and collaborators. The main dif ference is that all loops are coherently oriented and empty. The free energy is analytically evaluated and the continuum limit is analysed i n a region of parameters where the universality of the continuum descr iption may not be expected. Our phase diagram is analogous to Kazakov' s model with two phases (surface with small holes and tearing phase) w ith Kazakov's scaling exponents. The critical exponents of the third p hase, which occurs on the boundary between the two above phases, diffe r from the corresponding exponents in Kazakov's model [1].