Integrable Field Theory from Conformal Field Theory

Abstract

Equations of motion for two-dimensional quantum field theory obtained as some relevant perturbation around CFT are analyzed. It is shown that for particular degenerate fields taken as the perturbations, the resulting field theories posseses non-trivial local integrals of motion. The example is the scaling limit of the Ising model at $T = T_c$ but with non-vanishing magnetic field. Implications of the integrals of motion for corresponding particle theory are discussed and the exact S-matrix for the critical Ising model with magnetic field is conjectured.