Mass Scale in the Sine–gordon Model and Its Reductions

Known Bethe ansatz results about the sine–Gordon factorized scattering are reinterpreted in terms of perturbed conformal field theory. We obtain an exact relation between the ultraviolet and asymptotic scales (i.e. between the dimensional coupling constant and the soliton mass) and an explicit expression for the vacuum energy. The reduction technique then permits one to relate exactly the coupling constants and the mass scales in the Φ 13 -perturbed minimal CFT models. The preasymptotically free situation at β 2 near 8π is discussed on a preliminary footing.