(in collaboration with B. Eynard (CEA Saclay), M. Mulase (University of California, Davis) and B. Safnuk (McMaster University)) We constructed a one-matrix model for the generating function of a special class of coverings of CP_1, called simple coverings. Although relation between partition functions were known, it is usually not so easy to collect them by genus. The topological expansion of matrix models provides precisely an algorithm to do this. It is based on the knowledge of a complex curve (called the 'spectral curve' of the model), which we computed. This result answers a conjecture of V. Bouchard and M. Mariņo intuited from topological string theory consideration. (To be published) |
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