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

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

2010-11-09

arxiv.org/abs/1011.2207v2

SIGMA 7:023,2011

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.3842/SIGMA.2011.023

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.

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