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arXiv · hep-th/9108014

Loop Equations and the Topological Phase of Multi-Cut Matrix Models

C. Crnkovic·M. Douglas·G. Moore
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Abstract

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 $2\times 2$ 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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C. Crnkovic, M. Douglas, G. Moore. 1991-08-22. Loop Equations and the Topological Phase of Multi-Cut Matrix Models. https://doi.org/10.1142/s0217751x92003483

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