On the WDVV Equation and M-Theory

A wide class of Seiberg–Witten models constructed by M -theory techniques and described by non-hyperelliptic Riemann surfaces are shown to possess an associative algebra of holomorphic differentials. This is a first step towards proving that also these models satisfy the Witten–Dijkgraaf–Verlinde–Verlinde equation. In this way, similar results known for simpler Seiberg–Witten models (described by hyperelliptic Riemann surfaces and constructed without recourse to M -theory) are extended to certain non-hyperelliptic cases constructed in M -theory. Our analysis reveals a connection between the algebra of holomorphic differentials on the Riemann surface and the configuration of M -theory branes used in the construction of the corresponding Seiberg–Witten model.