N=4 Multi-Particle Mechanics, WDVV Equation and Roots
High Energy Physics - Theory
2011-05-13 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
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. Three ideas for classifying WDVV solutions are developed: ortho-polytopes, hypergraphs, and matroids. Various examples and counterexamples are displayed.
Keywords
Cite
@article{arxiv.1011.2207,
title = {N=4 Multi-Particle Mechanics, WDVV Equation and Roots},
author = {Olaf Lechtenfeld and Konrad Schwerdtfeger and Johannes Thürigen},
journal= {arXiv preprint arXiv:1011.2207},
year = {2011}
}