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arXiv · hep-th/0404249

WDVV equation and Triple-product Relation

Keiichi Shigechi·Miki Wadati·Ning Wang
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Abstract

We study the relation between the WDVV equations and the $τ$-function of the noncommutative KP (NCKP) hierarchy. WDVV-like equations (Hirota triple-product relation) in the noncommutative context appear as a consequence of the non-trivial equation for $τ$-function of the NC KP hierarchy, while the prepotential in the Seiberg-Witten (SW) theory has been identified to the $τ$-function of the Whitham hierarchy. We show that the spectral curve for the SW theory is the same as the Toda-chain hierarchy. We also show that Whitham hierarchy includes commutative Toda/KP hierarchy as a construction. Further, we comment on the origin of the Hirota triple-product relation in the context of the SW theory.

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Keiichi Shigechi, Miki Wadati, Ning Wang. 2004-04-30. WDVV equation and Triple-product Relation. https://doi.org/10.1016/j.nuclphysb.2004.11.060

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