N = 4 mechanics, WDVV equations and polytopes
Abstract
N = 4 superconformal nparticle 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, which can be encoded by particular polytopes. We provide A _{n} and B _{3} examples in some detail. Turning on the prepotential U in a given F background is very constrained for more than three particles and nonzero central charge. The standard ansatz for U is shown to fail for all finite Coxeter systems. Threeparticle models are more flexible and based on the dihedral root systems.
 Publication:

Physics of Atomic Nuclei
 Pub Date:
 February 2010
 DOI:
 10.1134/S1063778810020262
 arXiv:
 arXiv:0811.0021
 Bibcode:
 2010PAN....73..375L
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Talk at ISQS17 in Prague, 1921 June 2008, and at Group27 in Yerevan, 1319 August 2008