Mathematical Departments, University of Twente,

Computer Science building,

7500 AE Enschede, THE NETHERLANDS

E-mail: L.K.Hoevenaars@math.utwente.nl

**On the WDVV equations**

**Abstract:**

The original Witten-Dijkgraaf-Verlinde-Verlinde or WDVV equations form
a system of third order nonlinear partial differential equations playing
an important role in such areas as topological field theory, Frobenius
manifolds, quantum cohomology and integrable systems.

In the context of *N* = 2 supersymmetric Yang-Mills theory it was
realized by Marshakov, Mironov and Morozov that a suitable generalization
of the WDVV equations is necessary to identify the so-called prepotential
of the Yang-Mills theory as a solution to these equations. Typical solutions
(which are not solutions to the original equations) involve logarithmic
dependence on the variables.

We will introduce the original as well as the generalized WDVV equations
and present some exact solutions. In particular, inspired by *N* =
2 supersymmetric
Yang-Mills theory in five dimensions we obtain a set of functions with
trilogarithmic dependence which are surprisingly solutions to the original
(and not just the generalized) WDVV system.