Quantization of the N=2 supersymmetriC KdV hierarchy |
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Authors: | A M Zeitlin |
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Institution: | (1) St. Petersburg Department of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia |
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Abstract: | 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 precisely gives the monodromy matrix of the 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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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 303–314, May, 2006. |
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Keywords: | superconformal field theory quantum superalgebras supersymmetric KdV equation supersymmetric integrable systems quantization |
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