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

作者：Lechtenfeld Olaf^*; Schwerdtfeger Konrad; Thuerigen Johannes

来源：Symmetry Integrability and Geometry-Methods and Applications, 2011, 7: 023.

DOI：10.3842/SIGMA.2011.023

• superconformal mechanics
• Calogero models
• WDVV equation
• deformed root systems

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.

• 出版日期2011