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arXiv · hep-th/0312159

Integrable Structure of Superconformal Field Theory and Quantum super-KdV Theory

Petr P. Kulish·Anton M. Zeitlin
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Abstract

The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum version of the monodromy matrix associated with the linear problem for the corresponding L-operator is introduced. Using the explicit form of the irreducible representations of $\hat{osp}_q(1|2)$, the so-called "fusion relations" for the transfer matrices considered in different representations of $\hat{osp}_q(1|2)$ are obtained. The possible integrable perturbations of the model (primary operators, commuting with integrals of motion) are classified and the relation with the supersymmetric $\hat{osp}(1|2)$ Toda field theory is discussed.

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Petr P. Kulish, Anton M. Zeitlin. 2003-12-14. Integrable Structure of Superconformal Field Theory and Quantum super-KdV Theory. https://doi.org/10.1016/j.physletb.2003.12.008

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