Finite Size Effects in Integrable Quantum Field Theories

TL;DR

This paper explores finite size effects in integrable quantum field theories, using nonlinear integral equations to connect scattering data with conformal field theory, exemplified by Sine-Gordon and minimal models.

Contribution

It introduces a method based on nonlinear integral equations derived from Bethe Ansatz to analyze finite size effects and their relation to ultraviolet conformal field theories in integrable models.

Findings

Reconstruction of S-matrix from finite size data

Clarification of locality properties via Bethe root configurations

Application to Sine-Gordon and minimal models

Abstract

The study of Finite Size Effects in Quantum Field Theory allows the extraction of precious perturbative and non-perturbative information. The use of scaling functions can connect the particle content (scattering theory formulation) of a QFT to its ultraviolet Conformal Field Theory content. If the model is integrable, a method of investigation through a nonlinear integral equation equivalent to Bethe Ansatz and deducible from a light-cone lattice regularization is available. It allows to reconstruct the S-matrix and to understand the locality properties in terms of Bethe root configurations, thanks to the link to ultraviolet CFT guaranteed by the exact determination of scaling function. This method is illustrated in practice for Sine-Gordon / massive Thirring models, clarifying their locality structure and the issues of equivalence between the two models. By restriction of the Sine-Gordon model it is also possible to control the scaling functions of minimal models perturbed by Phi_1,3