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

TL;DR

This paper explores the integrable structures of superconformal field theory with supersymmetry, constructing quantum monodromy matrices via vertex operators, and discusses applications to perturbed models.

Contribution

It introduces a quantum monodromy matrix for SUSY N=1 KdV hierarchy using vertex operators and connects classical and quantum integrals of motion.

Findings

Classical integrals of motion match SUSY N=1 KdV hierarchy

Quantum monodromy matrix constructed via vertex operators

Potential applications to perturbed superconformal models

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.