caa a22 4500 467911630 CHVBK 20180406152850.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s11232-006-0065-x doi (NATIONALLICENCE)springer-10.1007/s11232-006-0065-x Marshakov A. Lebedev Physical Institute, RAS, Moscow, Russia aut Matrix models, complex geometry, and integrable systems: I [Elektronische Daten] [A. Marshakov] 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. Springer Science+Business Media, Inc., 2006 string theory nationallicence matrix models nationallicence complex geometry nationallicence Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 583-636 0040-5779 147:2<583 2006 147 11232 https://doi.org/10.1007/s11232-006-0065-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0065-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Marshakov A. Lebedev Physical Institute, RAS, Moscow, Russia aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/2(2006-05-01), 583-636 0040-5779 147:2<583 2006 147 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 467911533 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer