This article is cited in 11 papers

Matrix models, complex geometry, and integrable systems: I

A. V. Marshakov<sup>ab

a</sup> P. N. Lebedev Physical Institute, Russian Academy of Sciences
^b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: We consider the simplest gauge theories given by one- and two-matrix integrals and concentrate on their stringy and geometric properties. We recall the general integrable structure behind the matrix integrals and turn to the geometric properties of planar matrix models, demonstrating that they are universally described in terms of integrable systems directly related to the theory of complex curves. We study the main ingredients of this geometric picture, suggesting that it can be generalized beyond one complex dimension, and formulate them in terms of semiclassical integrable systems solved by constructing tau functions or prepotentials. We discuss the complex curves and tau functions of one- and two-matrix models in detail.

Keywords: string theory, matrix models, complex geometry.

Received: 09.10.2005

DOI: 10.4213/tmf1959

 English version: Theoretical and Mathematical Physics, 2006, 147:2, 583–636

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