Singular Vectors and Conservation Laws of Quantum KdV type equations

TL;DR

This paper establishes a direct link between vacuum singular vectors and conservation laws in quantum KdV equations, revealing quantum conserved quantities corresponding to classical ones at specific central charges, with various generalizations.

Contribution

It provides a direct proof of the relation between vacuum singular vectors and conservation laws in quantum KdV and extends the results to supersymmetric and Boussinesq cases.

Findings

Quantum conserved quantities match classical conservation laws at specific central charges.

The relation holds for various generalizations including supersymmetric and Boussinesq versions.

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.