N=4 mechanics, WDVV equations and roots

Understand

N=4 superconformal multi-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial differential equations linear in U and generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F.

• Putting U=0 yields a class of models (with zero central charge) which are encoded by the finite Coxeter root systems.
• We extend these WDVV solutions F in two ways: the A_n system is deformed n-parametrically to the edge set of a general orthocentric n-simplex, and the BCF-type systems form one-parameter families.
• A classification strategy is proposed.