Integrability of the quantum KdV equation at c = -2
We present a simple a direct proof of the complete integrability of the quantum KdV equation at $c=-2$, with an explicit description of all the conservation laws.
hep-th↗
arXiv subjects
P. Di Francesco
Publications and source records attributed to P. Di Francesco.
Singular Vectors and Conservation Laws of Quantum KdV type equations
We give a direct proof of the relation between vacuum singular vectors and conservation laws for the quantum KdV equation or equivalently for $Φ_{(1,3)}$-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.
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World Sheet and Space Time Physics in Two Dimensional (Super) String Theory
We show that tree level ``resonant'' $N$ tachyon scattering amplitudes, which define a sensible ``bulk'' S -- matrix in critical (super) string theory in any dimension, have a simple structure in two dimensional space time, due to partial decoupling of a certain infinite set of discrete states. We also argue that the general (non resonant) amplitudes are determined by the resonant ones, and calculate them explicitly, finding an interesting analytic structure. Finally, we discuss the space time interpretation of our results.
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