WDVV solutions from orthocentric polytopes and Veselov systems
High Energy Physics - Theory
2008-06-26 v2 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0805.3245,
title = {WDVV solutions from orthocentric polytopes and Veselov systems},
author = {Olaf Lechtenfeld},
journal= {arXiv preprint arXiv:0805.3245},
year = {2008}
}
Comments
1+10 pages, 3 figures, contribution to a volume in honor of Ioseph L. Buchbinder; v2: minor corrections in sect.5