Perturbation theory around two-dimensional critical systems through holomorphic decomposition

Abstract

The authors consider perturbations by relevant interactions of two-dimensional conformally invariant rational field theories. The meromorphic structure-with respect to the scaling dimensions of the perturbing interactions-of the correlation functions is made explicit through a successive application of Stoke's theorem. The resulting decomposition of the amplitudes into holomorphic and antiholomorphic factors yields a representation of the meromorphic structure in terms of the basic data of the rational field theory, which are scaling dimensions, operator product coefficients and braid matrices. They exemplify the general deduction by a concrete calculation to the third order in the coupling constant of the perturbing interaction.