WDVV equation and Triple-product Relation

Details WDVV equation and Triple-product Relation WDVV equation and Triple-product Relation

2004-04-30

arxiv.org/abs/hep-th/0404249v1

Nucl.Phys. B706 (2005) 518-530

Physics

High Energy Physics

High Energy Physics - Theory

Latex,11 pages,no figures

Scientific paper

10.1016/j.nuclphysb.2004.11.060

We study the relation between the WDVV equations and the $\tau$-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 $\tau$-function of the NC KP hierarchy, while the prepotential in the Seiberg-Witten (SW) theory has been identified to the $\tau$-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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