In Seiberg–Witten theory the solutions to these equations come in certain classes according to the gauge group. We show that the duality transformations transform solutions within a class to another solution within the same class, by using a subset of the Picard–Fuchs equations on the Seiberg–Witten family of Riemann surfaces. The electric–magnetic duality transformations can be thought of as changes of a canonical homology basis on the surfaces which in our derivation is clearly responsible for the covariance of the generalized WDVV system.
- WDVV equations
- Seiberg–Witten theory