N=2 and N=4 Supersymmetric mKdV and sinh-Gordon Hierarchies

H. Aratyn; J. F. Gomes; L. H. Ymai; A. H. Zimerman

paper

N=2 and N=4 Supersymmetric mKdV and sinh-Gordon Hierarchies

arXiv:hep-th/0409171

Abstract

Integrable models with higher N=2 and N=4 supersymmetries are formulated on reductions of twisted loop superalgebras $s l^(2∣2)$ and $s l^(4∣4)$ endowed with principal gradation. In case of the $s l^(4∣4)$ loop algebra a sequence of progressing reductions leads both to the N=4 and N=2 supersymmetric mKdV and sinh-Gordon equations. The reduction scheme is induced by twisted automorphism and allows via dressing approach to associate to each symmetry flow of half-integer degree a supersymmetry transformation involving only local expressions in terms of the underlying fields.

25 pages