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

H. Aratyn·J. F. Gomes·L. H. Ymai·A. H. Zimerman
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Abstract

Integrable models with higher N=2 and N=4 supersymmetries are formulated on reductions of twisted loop superalgebras $\hat{sl}(2|2)$ and $\hat{sl}(4|4) $ endowed with principal gradation. In case of the $\hat{sl}(4|4)$ 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.

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H. Aratyn, J. F. Gomes, L. H. Ymai, A. H. Zimerman. 2004-09-16. N=2 and N=4 Supersymmetric mKdV and sinh-Gordon Hierarchies. https://arxiv.org/abs/hep-th/0409171

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