On Integrable Structure behind the Generalized WDVV Equations

Abstract

In the theory of quantum cohomologies the WDVV equations imply integrability of the system $(I{\partial }_{\mu }-z{C}_{\mu })\psi =0$. 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 $\psi$ appear inconsistent. Instead they are substituted by $(C_{\mu }{\partial }_{\nu }-C_{\nu }{\partial }_{\mu }){\psi }^{(\mu )}\sim (F_{\mu }{\partial }_{\nu }-F_{\nu }{\partial }_{\mu }){\psi }^{(\mu )}=0$, where matrices $(F_{\mu }{)}_{\alpha \beta }={\partial }_{\alpha }{\partial }_{\beta }{\partial }_{\mu }F$.

LaTeX, 6pp

References in corpus (1)

• WDVV Equations from Algebra of Forms

Cited by in corpus (5)

• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
• Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case
• Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations
• WDVV Equations as Functional Relations