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arXiv · hep-th/9711194

On Integrable Structure behind the Generalized WDVV Equations

A. Morozov
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Abstract

In the theory of quantum cohomologies the WDVV equations imply integrability of the system $(I\partial_μ- zC_μ)ψ= 0$. However, in generic situation -- of which an example is provided by the Seiberg-Witten theory -- there is no distinguished direction (like $t^0$) in the moduli space, and such equations for $ψ$ appear inconsistent. Instead they are substituted by $(C_μ\partial_ν- C_ν\partial_μ)ψ^{(μ)} \sim (F_μ\partial_ν- F_ν\partial_μ)ψ^{(μ)} = 0$, where matrices $(F_μ)_{αβ} = \partial_α\partial_β\partial_μF$.

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A. Morozov. 1997-11-26. On Integrable Structure behind the Generalized WDVV Equations. https://doi.org/10.1016/s0370-2693(98)00314-1

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