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arXiv · hep-th/9509162

Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory

Toshio Nakatsu·Kanehisa Takasaki
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Abstract

The exact solution of $N=2$ supersymmetric $SU(N)$ Yang-Mills theory is studied in the framework of the Whitham hierarchies. The solution is identified with a homogeneous solution of a Whitham hierarchy. This integrable hierarchy (Whitham-Toda hierarchy) describes modulation of a quasi-periodic solution of the (generalized) Toda lattice hierarchy associated with the hyperelliptic curves over the quantum moduli space. The relation between the holomorphic pre-potential of the low energy effective action and the $τ$ function of the (generalized) Toda lattice hierarchy is also clarified.

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Toshio Nakatsu, Kanehisa Takasaki. 1995-09-28. Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory. https://doi.org/10.1142/s0217732396000187

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