Quantization of the N=2 Supersymmetric KdV Hierarchy

Details Quantization of the N=2 Supersymmetric KdV Hierarchy Quantization of the N=2 Supersymmetric KdV Hierarchy

2006-06-14

arxiv.org/abs/hep-th/0606129v1

Theor.Math.Phys.147:698-708,2006; Teor.Mat.Fiz.147:303-314,2006

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 12 pages

Scientific paper

10.1007/S11232-006-0071-Z

We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the $sl^{(1)}(2|1)$ affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that in the classical limit, this object gives the monodromy matrix of N=2 supersymmetric KdV system. We also show that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under two supersymmetry transformations and the zero mode of the associated U(1) current.

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