Geodesic
Matrix models, complex geometry, and integrable
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 163-228 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. V. Marshakov. Matrix models, complex geometry, and integrable. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 163-228. http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a0/

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