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Integrable hierarchies in Donaldson-Witten and Seiberg-Witten theories

Jose D. Edelstein·Marta Gomez-Reino
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Abstract

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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Jose D. Edelstein, Marta Gomez-Reino. 2000-10-09. Integrable hierarchies in Donaldson-Witten and Seiberg-Witten theories. https://arxiv.org/abs/hep-th/0010061

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