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Comment: 5 pages; v2: minor clarifications, refs. added, version published in PRD
Comment: 1+20 pages, v2: typos fixed, for publication in JHEP
Comment: 1+28 pages, no figures; v2: clarifying remarks and references added, published version
Comment: 12 pages, talk presented by E.Ivanov at the XIII International Conference "Symmetry Methods in Physics", Dubna, July 6-9, 2009
Comment: 1+8 pages; v2: two references added, published version
Comment: 8 pages; v2: references added, typos fixed, version for PLA
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.
Comment: 1+16 pages; v2: example of section 5 changed to R_xi gauges; v3: small corrections to section 5, one reference added, published version
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