WDVV solutions from orthocentric polytopes and Veselov systems

Abstract

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.

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

References in corpus (4)

• N=4 superconformal Calogero models
• N=4 mechanics, WDVV equations and roots
• On geometry of a special class of solutions to generalised WDVV equations
• On the geometry of V-systems

Cited by in corpus (6)

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• N=4 Multi-Particle Mechanics, WDVV Equation and Roots
• Remarks on Multi-Dimensional Conformal Mechanics
• A new class of solutions to the WDVV equation