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.
Physics of Atomic Nuclei
- Pub Date:
- February 2010
- High Energy Physics - Theory;
- Mathematical Physics
- Talk at ISQS-17 in Prague, 19-21 June 2008, and at Group-27 in Yerevan, 13-19 August 2008