LOOP EQUATIONS AND THE TOPOLOGICAL PHASE OF MULTICUT MATRIX MODELS

We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy of flows of 2 X 2 matrices. We derive from it loop equations which can be expressed as Virasoro constraints on the partition function. We discover a ''pure topological'' phase of the theory in which all correlation functions are determined by recursion relations. We also examine macroscopic loop amplitudes, which suggest a relation to 2D gravity coupled to dense polymers.