id: 05909789
dt: j
an: 05909789
au: Lechtenfeld, Olaf; Schwerdtfeger, Konrad; Thürigen, Johannes
ti: $N=4$ multi-particle mechanics, WDVV equation and roots.
so: SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 023, 21 p.,
    electronic only (2011).
py: 2011
pu: Department of Applied Research, Institute of Mathematics of National
    Academy of Sciences of Ukraine, Kyiv
la: EN
cc: 
ut: superconformal mechanics; Calogero models; WDVV equation; deformed root
    systems
ci: 
li: doi:10.3842/SIGMA.2011.023
ab: Summary: 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.
rv: