On the WDVV equation and M-theory

A wide class of Seiberg-Witten models constructed by M-theory techniques an d described by non-hyperelliptic Riemann surfaces are shown to possess an a ssociative algebra of holomorphic differentials. This is a first step towar ds proving that also these models satisfy the Witten-Dijkgraaf-Verlinde-Ver linde equation. In this way, similar results known for simpler Seiberg-Witt en models (described by hyperelliptic Riemann surfaces and constructed with out recourse to M-theory) are extended to certain non-hyperelliptic cases c onstructed in M-theory. Our analysis reveals a connection between the algeb ra of holomorphic differentials on the Riemann surface and the configuratio n of M-theory branes of the corresponding Seiberg-Witten model. (C) 1999 El sevier Science B.V.