Singular Vectors and Conservation Laws of Quantum KdV type equations

Abstract

We give a direct proof of the relation between vacuum singular vectors and conservation laws for the quantum KdV equation or equivalently for ${\Phi }_{(1,3)}$-perturbed conformal field theories. For each degree at which a classical conservation law exists, we find a quantum conserved quantity for a specific value of the central charge. Various generalizations ($N=1,2$ supersymmetric, Boussinesq) of this result are presented.

9 pages

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