arXiv subjects
Publications and source records attributed to L. K. Hoevenaars.
We give a short review of Frobenius manifolds and algebraic integrability and study their intersection. The simplest case is the relation between the Frobenius manifold of simple singularities, which is almost dual to the integrable open Toda chain. New types of manifolds called extra special Kaehler and special F-manifolds are introduced which capture the intersection.
We construct second order reductions of the generalized Witten-Dijkgraaf-Verlinde-Verlinde system based on simple Lie algebras. We discuss to what extent some of the symmetries of the WDVV system are preserved by the reduction.
By introduction of an additional variable and addition of a Weyl invariant correction term to the perturbative prepotential in five-dimensional Seiberg-Witten theory we construct solutions of the WDVV equations of trigonometric type for all crystallographic root systems.
It is well-known that the perturbative prepotentials of four-dimensional N=2 supersymmetric Yang-Mills theories satisfy the generalized WDVV equations, regardless of the gauge group. In this paper we study perturbative prepotentials of the five-dimensional theories for some classical gauge groups and determine whether or not they satisfy the WDVV system.
A proof that the prepotential for pure N=2 Super-Yang-Mills theory associated with Lie algebras B_r and C_r satisfies the generalized WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) system was given by Marshakov, Mironov and Morozov. Among other things, they use an associative algebra of holomorphic differentials. Later Ito and Yang used a different approach to try to accomplish the same result, but they encountered objects of which it is unclear whether they form structure constants of an associative algebra. We show by explicit calculation that these objects are none other than the structure constants of the algebra of holomorphic differentials.
An associative algebra of holomorphic differential forms is constructed associated with pure N=2 Super-Yang-Mills theory for the Lie algebra F4. Existence and associativity of this algebra, combined with the general arguments in the work of Marshakov, Mironov and Morozov, proves that the prepotential of this theory satisfies the generalized WDVV system.