Quantum integrability of perturbed Virasoro-degenerate conformal models

Off-critical conservation laws of a class of irrational conformal models are examined. It has been conjectured that he massive theories that arise under perturbation with the energy (respectively spin-density) operator possess an infinite number of conser-vation laws, constructable in the Hilbert space of the CFT. A constructive proof of this conjecture is given by means of an algo-rithmic Fock space procedure. A distinctive feature of 2-dimensional conformal field theory (CFT) is the clear-cut factorization of the the-pry into right- and left-moving lightcone sectors. To a large extent he solution of a CFT can then be traced back to the representation theory of infinite dimensional Lie algebras. Whenever such a factorization cannot be achieved a priory, i.e. left-and right-movers mix in an essential way, most of the stringent algebraic structure seems to be lost. As part of his program [1-4] to study the scaling region around a CFT, Zamolodchikov pro-posed in ref. [ 5] that the off-critical behavior of certain CFTs, perturbed by suitable relevant operators, hould be governed by an infinite number of conserved currents of higher spin N>_-2. The latter can be taken as a pragmatic definition of integrability. These currents are solutions of the compatibility relation for the mappin