Olaf Lechtenfeld (Hannover):
N=4 mechanics, WDVV equations and roots
N=4 superconformal $n$-particle quantum mechanics on the real line
is governed by two prepotentials, U and F, which obey a system of
partial nonlinear differential equations generalizing the
Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F.
The solutions are encoded by the finite Coxeter systems and
certain deformations thereof. Nonvanishing U (and central charge)
occurs only for the SU(2) and the even dihedral root systems.
Thus, up to coordinate change and orthogonal composition, tunable
couplings occur only in peculiar three-particle models, among which
the one based on G_2+A_1 is the prime example.