Superconformal Field Theory and SUSY N=1 KdV Hierarchy I: Vertex Operators and Yang-Baxter Equation

Abstract

The supersymmetry invariant integrable structure of two-dimensional superconformal field theory is considered. The classical limit of the corresponding infinite family of integrals of motion (IM) coincide with the family of IM of SUSY N=1 KdV hierarchy. The quantum version of the monodromy matrix, generating quantum IM, associated with the SUSY N=1 KdV is constructed via vertex operator representation of the quantum R-matrix. The possible applications to the perturbed superconformal models are discussed.

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

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• Integrability of a family of quantum field theories related to sigma models
• Affine Yangian of $\mathfrak{gl}(2)$ and integrable structures of superconformal field theory
• Quantum Supersymmetric Toda-mKdV Hierarchies
• ODE/IM correspondence and supersymmetric affine Toda field equations
• Q-operator and fusion relations for $C_q^{(2)}(2)$
• 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
• The ODE/IM Correspondence between $C(2{)}^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish