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Supersymmetry and the KdV equations for Integrable Hierarchies with a Half-integer Gradation

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

Supersymmetry is formulated for integrable models based on the $sl(2|1)$ loop algebra endowed with a principal gradation. The symmetry transformations which have half-integer grades generate supersymmetry. The $sl(2|1)$ loop algebra leads to N=2 supersymmetric mKdV and sinh-Gordon equations. The corresponding N=1 mKdV and sinh-Gordon equations are obtained via reduction induced by twisted automorphism. Our method allows for a description of a non-local symmetry structure of supersymmetric integrable models.

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H. Aratyn, J. F. Gomes, A. H. Zimerman. 2003-09-09. Supersymmetry and the KdV equations for Integrable Hierarchies with a Half-integer Gradation. https://doi.org/10.1016/j.nuclphysb.2003.10.021

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