WDVV solutions from orthocentric polytopes and Veselov systems

Details WDVV solutions from orthocentric polytopes and Veselov systems WDVV solutions from orthocentric polytopes and Veselov systems

2008-05-21

arxiv.org/abs/0805.3245v2

Physics

High Energy Physics

High Energy Physics - Theory

1+10 pages, 3 figures, contribution to a volume in honor of Ioseph L. Buchbinder; v2: minor corrections in sect.5

Scientific paper

N=4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation. For U=0 one remains with the WDVV equation which suggests an ansatz for F in terms of a set of covectors to be found. One approach constructs such covectors from suitable polytopes, another method solves Veselov's \vee-conditions in terms of deformed Coxeter root systems. I relate the two schemes for the A_n example.

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