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

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

2003-09-09

arxiv.org/abs/hep-th/0309099v1

Nucl.Phys. B676 (2004) 537-571

Physics

High Energy Physics

High Energy Physics - Theory

35 pgs., latex

Scientific paper

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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