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

Abstract

The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\widehat{osp}(1|2)$ 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 ${\widehat{osp}}_q(1|2)$, the so-called "fusion relations" for the transfer matrices considered in different representations of ${\widehat{osp}}_q(1|2)$ are obtained. The possible integrable perturbations of the model (primary operators, commuting with integrals of motion) are classified and the relation with the supersymmetric $\widehat{osp}(1|2)$ Toda field theory is discussed.

arXiv commentLaTeX2e, elsart.cls, 11 pages, subm. to Physics Letters B

References in corpus (3)

• Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz
• Generalized KdV and Quantum Inverse Scattering Description of Conformal Minimal Models
• Trigonometric osp(1|2) Gaudin model

Cited by in corpus (8)

• Superconformal Field Theory and SUSY N=1 KdV Hierarchy II: The Q-operator
• Superconformal Field Theory and SUSY N=1 KdV Hierarchy I: Vertex Operators and Yang-Baxter Equation
• Integrability of a family of quantum field theories related to sigma models
• Quantum Supersymmetric Toda-mKdV Hierarchies
• Integrability of Superconformal Field Theory and SUSY N=1 KdV
• Quantization of the N=2 Supersymmetric KdV Hierarchy
• Quantum Inverse Scattering Method and (Super)Conformal Field Theory
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish