Quantization of the $N{=}2$ supersymmetric $\text{KdV}$ hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 303-314
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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
Mots-clés : quantization.
Mots-clés : quantization.
@article{TMF_2006_147_2_a6,
author = {A. M. Zeitlin},
title = {Quantization of the $N{=}2$ supersymmetric $\text{KdV}$ hierarchy},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {303--314},
publisher = {mathdoc},
volume = {147},
number = {2},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a6/}
}
A. M. Zeitlin. Quantization of the $N{=}2$ supersymmetric $\text{KdV}$ hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 2, pp. 303-314. http://geodesic.mathdoc.fr/item/TMF_2006_147_2_a6/