Mass Generation in Perturbed Massless Integrable Models

We extend form-factor perturbation theory to non–integrable deformations of mass-less integrable models, in order to address the problem of mass generation in such systems. With respect to the standard renormalisation group analysis this approach is more suitable for studying the particle content of the perturbed theory. Analogously to the massive case, interesting information can be obtained already at first order, such as the identification of the operators which create a mass gap and those which induce the confinement of the massless particles in the perturbed theory. Introduction. Given the large number of remarkable results obtained from the study of two–dimensional integrable quantum field theories (IQFTs), at present one of the most interesting challenges consists of developing a systematic approach to study non-integrable models, at least when they are deformations of integrable ones. For massive field theories a convenient perturbative scheme, based on the exact knowledge of the form-factors (FFs) of the original integrable theory, was suggested in [1]. Already at first order, it proved able to provide a great deal of information, such as the evolution of the particle content, the variation of the masses and the change of the ground state energy – results successfully checked by numerical studies. The main purpose of this paper is to extend Form Factor Perturbation Theory (FFPT) to non–integrable deformations of massless IQFTs. The most fundamental question that one may ask in this context is whether a perturbation creates a gap in the excitation spectrum – a problem usually addressed via the renormalisation group (RG) equations near a fixed point [2]. Moreover, if massive particles are created, one would like to understand whether they are adiabatically related to the original massless excitations or, like in the massive case, confinement takes place. Since the RG eq.s cannot provide a complete answer to any of the above questions, it is worth exploring other alternative routes. The FFPT relies directly on the particle description of the unperturbed theory and, for this reason, it seems to be the most natural and suitable approach for studying the evolution of the particle content when the perturbation is switched on. Our analysis is presently limited to the first order of FFPT, its extension to higher orders being, as in the massive case, an interesting but non-trivial mathematical problem. Despite the fact that one must be careful in handling results at such low order, some useful conclusions can nevertheless be reached. …