Matrix models, complex geometry, and integrable systems: I |
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Authors: | A V Marshakov |
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Institution: | (1) Lebedev Physical Institute, RAS, Moscow, Russia;(2) Institute for Theoretical and Experimental Physics, Moscow, Russia |
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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.
This article was written at the request of the Editorial Board. It is based on several lectures presented at schools of mathematical
physics and talks at the conference “Complex Geometry and String Theory” and the Polivanov memorial seminar.]
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 163–228, May, 2006. |
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Keywords: | string theory matrix models complex geometry |
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