Seiberg-Witten Theory and Extended Toda Hierarchy

Abstract

The quasiclassical solution to the extended Toda chain hierarchy, corresponding to the deformation of the simplest Seiberg-Witten theory by all descendants of the dual topological string model, is constructed explicitly in terms of the complex curve and generating differential. The first derivatives of prepotential or quasiclassical tau-function over the extra times, extending the Toda chain, are expressed through the multiple integrals of the Seiberg-Witten one-form. We derive the corresponding quasiclassical Virasoro constraints, discuss the functional formulation of the problem and propose generalization of the extended Toda hierarchy to the nonabelian theory.

32 pages, LaTeX

References in corpus (2)

• Extended Seiberg-Witten Theory and Integrable Hierarchy
• On Microscopic Origin of Integrability in Seiberg-Witten Theory

Cited by in corpus (6)

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• Tau-functions for Quiver Gauge Theories
• Low Energy Processes Associated with Spontaneously Broken N=2 Supersymmetry
• On two-dimensional quantum gravity and quasiclassical integrable hierarchies