Complex Geometry of Matrix Models

Details Complex Geometry of Matrix Models Complex Geometry of Matrix Models

2005-06-09

arxiv.org/abs/hep-th/0506075v1

Proc.Steklov Inst.Math.251:254-292,2005

Physics

High Energy Physics

High Energy Physics - Theory

36 pages

Scientific paper

The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by quasiclassical or generalized Whitham hierarchies and are directly related to the superpotentials of four-dimensional N=1 SUSY gauge theories. We study the derivatives of tau-functions for these solutions, associated with the families of Riemann surfaces (with possible double points), and relations for these derivatives imposed by complex geometry, including the WDVV equations. We also find the free energy in subleading order of the 't Hooft expansion and prove that it satisfies certain determinant relations.

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