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This article is cited in 4 scientific papers (total in 4 papers)
Quantization of the $N{=}2$ supersymmetric $\text{KdV}$ hierarchy
A. M. Zeitlin St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
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{\rm)} is invariant under
two supersymmetry transformations and the zero mode of the associated $U(1)$
current.
Keywords:
superconformal field theory, quantum superalgebras, supersymmetric KdV equation, supersymmetric integrable systems, quantization.
Received: 19.09.2005 Revised: 16.11.2005
Citation:
A. M. Zeitlin, “Quantization of the $N{=}2$ supersymmetric $\text{KdV}$ hierarchy”, TMF, 147:2 (2006), 303–314; Theoret. and Math. Phys., 147:2 (2006), 698–708
Linking options:
https://www.mathnet.ru/eng/tmf1965https://doi.org/10.4213/tmf1965 https://www.mathnet.ru/eng/tmf/v147/i2/p303
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