Sergey Krivonos, Olaf Lechtenfeld
We overcome the barrier of constructing N=4 superconformal models in one
space dimension for more than three particles. The D(2,1;alpha) superalgebra of
our systems is realized on the coordinates and momenta of the particles, their
superpartners and one complex pair of harmonic variables. The models are
determined by two prepotentials, F and U, which must obey the WDVV and a
Killing-type equation plus homogeneity conditions. We investigate
permutation-symmetric solutions, with and without translation invariance.
Models based on deformed A_n and BCD_n root systems are constructed for any
value of alpha, and exceptional F_n-type and super root systems admit solutions
as well. Translation-invariant mechanics occurs for any number of particles at
alpha=-1/2 (osp(4|2) invariance as a degenerate limit) and for four particles
at arbitrary alpha (three series).
View original:
http://arxiv.org/abs/1012.4639
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