A Matrix Model for Random Surfaces with Dynamical

A matrix model to describe dynamical loops on random planar graphs is analyzed. It has similarities with a model studied by Kazakov, few years ago, and the O(n) model by Kostov and collaborators. The main diierence is that all loops are coherently oriented and empty. The free energy is analytically evaluated and the two critical phases are analyzed, where the free energy exhibits the same critical behaviour of Kazakov's model, thus connrming the universality of the description in the continuum limit (surface with small holes, and the tearing phase). A third phase occurs on the boundary separating the above phase regions, and is characterized by a diierent singular behaviour.