Loop Equations and the Topological Phase of Multi - Cut Matrix Models
نویسندگان
چکیده
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× 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.
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