Integrable Hierarchies in Donaldson-Witten and Seiberg-Witten Theories [chapter]

J. D. Edelstein, M. Gómez-Reino
2001 Integrable Hierarchies and Modern Physical Theories  
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 τ -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 τ -function corresponding to a multisoliton solution. We obtain a new expression for the contact terms that links these results to the
more » ... se results to the Whitham hierarchy formulation of Seiberg-Witten theories.
doi:10.1007/978-94-010-0720-7_2 fatcat:bqug76qyezdfblhds23m3rge44