N=4 Multi-Particle Mechanics, WDVV Equation and Roots

Understand

We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U.

• The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed flat Yang-Mills connections.
• Three- and four-particle solutions are presented.
• The covector ansatz turns the WDVV equation into an algebraic condition, for which we give a formulation in terms of partial isometries.