N=4 Mechanics, WDVV Equations and Polytopes

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 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.

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

References in corpus (4)

• N=4 superconformal Calogero models
• N=4 mechanics, WDVV equations and roots
• New insight into WDVV equation
• Locus configurations and $\vee$-systems

Cited by in corpus (1)

• Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\ell$- and $\tilde{\ell }$-Equivalence Classes