Form-Factor Bootstrap and the Operator Content of Perturbed Minimal Models.pdf

a r X i v : h e p - t h / 9 4 0 5 0 1 4 v 3 2 3 A u g 1 9 9 4 DAMTP-HEP-94/15 Form-Factor Bootstrap and the Operator Content of Perturbed Minimal Models A. Koubek? Department of Applied Mathematics and Theoretical Physics, Silver Street, CB3 9EW Cambridge, UK Abstract The form-factor bootstrap approach is applied to the perturbed minimal models M2,2n+3 in the direction of the primary field φ1,3. These theories are integrable and contain n massive scalar particles, whose S–matrix is purely elastic. The form- factor equations do not refer to a specific operator. We use this fact to classify the operator content of these models. We show that the perturbed models contain the same number of primary fields as the conformal ones. Explicit solutions are constructed and conjectured to correspond to the off-critical primary fields φ1,k. May 1994 revised version ?E-mail: a.koubek@amtp.cam.ac.uk 1 Introduction The identification of local operators in a given model and the computation of their multi- point correlators is one of the most important problems in Quantum Field Theory (QFT). For two-dimensional critical QFT, a successful approach is given by the conformal boot- strap analysis [1, 2, 3, 4, 5, 6] . The operator content of such theories consists of a set of conformal families which form irreducible representations of the conformal Virasoro alge- bra. The representatives of these families, organized in a tower of descendant operators of increasing anomalous dimensions and spin, are identified by their primary operators. The number of conformal families is finite for the so-called minimal models. Using the representation theory of the underlying Virasoro (or higher dimensional) algebra, it turns out that the correlation functions of conformal operators in the minimal models can be written as solutions of linear differential equations [2, 7]. Concerning the massive integrable QFT, the present understanding is incomplete, though much progress has been achieved recently.