N=4 Mechanics, WDVV Equations and Polytopes - High Energy Physics - TheoryReport as inadecuate




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Abstract: N=4 superconformal n-particle quantum mechanics on the real line is governedby two prepotentials, U and F, which obey a system of partial nonlineardifferential equations generalizing the Witten-Dijkgraaf-Verlinde-VerlindeWDVV equation for F.
The solutions are encoded by the finite Coxeter systemsand 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 Uin a given F background is very constrained for more than three particles andnonzero central charge.
The standard ansatz for U is shown to fail for allfinite Coxeter systems.
Three-particle models are more flexible and based onthe dihedral root systems.



Author: Olaf Lechtenfeld

Source: https://arxiv.org/



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