Many-particle mechanics with D(2,1;alpha) superconformal symmetry
Abstract
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).
Keywords
Cite
@article{arxiv.1012.4639,
title = {Many-particle mechanics with D(2,1;alpha) superconformal symmetry},
author = {Sergey Krivonos and Olaf Lechtenfeld},
journal= {arXiv preprint arXiv:1012.4639},
year = {2012}
}
Comments
1+12 pages, no figures; v2: two refs added, typos corrected, version published in JHEP; v3: minor correction to (3.8) & (3.10)