Loops in the Curvature Matrix Model

Abstract

Macroscopic loop correlators are investigated in the hermitian one matrix model with the potential perturbed by the higher order curvature term. In the phase of smooth surfaces the model is equivalent to the minimal conformal matter coupled to gravity. The properties of the model in the intermediate phase are similar to that of the discretized bosonic string with the central charge $C > 1.$ Loop correlators describe the effect of the splitting of the random surfaces. It is shown, that the properties of the surfaces are changed in the intermediate phase because the perturbation modifies the spectrum of the scaling operators.