On the WDVV Equation and M-Theory

Abstract

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 of the corresponding Seiberg-Witten model.

30 pages, Latex, some corrections made, refs added

References in corpus (3)

• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• N=2 SYM RG Scale as Modulus for WDVV Equations
• Beta Function, C--Theorem and WDVV Equations in 4D N=2 SYM

Cited by in corpus (7)

• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• DV and WDVV
• Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case
• Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation
• Large N gauge theories and topological cigars
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• A Surprising Relation for the Effective Coupling Constants of N=2 Super Yang-Mills Theories