Geometry and Integrability in Mathematical Physics GIMP'06
May 15 - 19, 2006, Moscow, Russia
Andrei Marshakov
ITEP, Moscow
Microscopic setup and effective geometry of the Seiberg-Witten theory
We present the geometric framework for the Seiberg-Witten theory in terms of integrable systems. We point out the microscopic origin of the Seiberg-Witten theory, given by Nekrasov instantonic calculations for the partition function, and resulting in the effective "matrix model picture" for the Seiberg-Witten prepotentials. The dependence of the macroscopic complex geometry on the flows, corresponding to the perturbations of the microscopic theory, is solved for the parameters of Seiberg-Witten curves in terms of quasiclassical Toda hierarchies. The corresponding solution can be also interpreted in terms of the dual Gromov-Witten theory of the topological strings.
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