Kink scaling functions in 2D non--integrable quantum field theories

We determine the semiclassical energy levels for the \phi^4 field theory in the broken symmetry phase on a 2D cylindrical geometry with antiperiodic boundary conditions by quantizing the appropriate finite–volume kink solutions. The analytic form of the kink scaling functions for arbitrary size of the system allows us to describe the flow between the twisted sector of c=1 CFT in the UV region and the massive particles in the IR limit. Kink-creating operators are shown to correspond in the UV limit to disorder fields of the c=1 CFT. The problem of the finite–volume spectrum for generic 2D Landau–Ginzburg models is also discussed.