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Article

Topological strings, matrix integrals, and singularity theory.

Nakatsu T., Kato A., Noumi M., Takebe T.

We study the relation between topological string theory and singularity theory using the partition function of A_N-1 topological string defined by matrix integral of Kontsevich type. Genus expansion of the free energy is considered, and the genus g=0 contribution is shown to be described by a special solution of N-reduced dispersionless KP system. We show a universal correspondences between the time variables of dispersionless KP hierarchy and the flat coordinates associated with versal deformations of simple singularities of type A. We also study the behavior of topological matter theory on the sphere in a topological gravity background, to clarify the role of the topological string in the singularity theory. Finally we make some comment on gravitational phase transition.