N=4 Mechanics, WDVV Equations and Polytopes

Details N=4 Mechanics, WDVV Equations and Polytopes N=4 Mechanics, WDVV Equations and Polytopes

2008-11-03

arxiv.org/abs/0811.0021v2

Physics

High Energy Physics

High Energy Physics - Theory

Talk at ISQS-17 in Prague, 19-21 June 2008, and at Group-27 in Yerevan, 13-19 August 2008; v2: B_3 examples corrected

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 F. The solutions are encoded by the finite Coxeter systems and certain deformations thereof, which can be encoded by particular polytopes. We provide A_n and B_3 examples in some detail. Turning on the prepotential U in a given F background is very constrained for more than three particles and nonzero central charge. The standard ansatz for U is shown to fail for all finite Coxeter systems. Three-particle models are more flexible and based on the dihedral root systems.

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