Integrable hierarchies in Donaldson-Witten and Seiberg-Witten theories

Details Integrable hierarchies in Donaldson-Witten and Seiberg-Witten theories Integrable hierarchies in Donaldson-Witten and Seiberg-Witten theories

2000-10-09

arxiv.org/abs/hep-th/0010061v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 1 figure, LaTeX2e/Kluwer style files included, Invited Talk at the NATO Advanced Research Workshop "Integrable Hiera

Scientific paper

We review various aspects of integrable hierarchies appearing in N=2 supersymmetric gauge theories. In particular, we show that the blowup function in Donaldson-Witten theory, up to a redefinition of the fast times, is a tau function for a g-gap solution of the KdV hierarchy. In the case of four-manifolds of simple type, instead, the blowup function becomes a tau function corresponding to a multisoliton solution. We obtain a new expression for the contact terms that links these results to the Whitham hierarchy formulation of Seiberg-Witten theories.

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