Integrable structure behind the generalized WDVV equations

In the theory of quantum cohomologies the WDVV equations imply integrability of the system (I∂μ−zCμ)ψ=0. However, in generic situation – of which an example is provided by the Seiberg-Witten theory – there is no distinguished direction (like t0) in the moduli space, and such equations for ψ appear inconsistent. Instead they are substituted by (Cμ∂ν−Cν∂μ)ψ∼(Fμ∂ν−Fν∂μ)ψ=0, where matrices (Fμ)αβ=∂α∂β∂μF.