Matrix Models, Complex Geometry and Integrable Systems. II

TL;DR

This paper explores the geometric and integrable structures of matrix models, focusing on nonlinear differential equations of tau-functions and their applications in supersymmetric gauge theories and AdS/CFT correspondence.

Contribution

It extends previous methods to new applications in gauge theories and string theory, highlighting the geometric interpretation of integrability in these contexts.

Findings

Derivation of nonlinear differential equations for quasiclassical tau-functions

Identification of geometric structures in supersymmetric gauge theories

Connections established between matrix models and AdS/CFT correspondence

Abstract

We consider certain examples of applications of the general methods, based on geometry and integrability of matrix models, described in hep-th/0601212. In particular, the nonlinear differential equations, satisfied by quasiclassical tau-functions are investigated. We also discuss a similar quasiclassical geometric picture, arising in the context of multidimensional supersymmetric gauge theories and the AdS/CFT correspondence.