Non-integrable aspects of the multi-frequency Sine-Gordon model

TL;DR

This paper analyzes how non-integrable perturbations in a multi-frequency Sine-Gordon model affect particle spectra, soliton confinement, and phase flows, using Form Factor Perturbation Theory with applications to related models.

Contribution

It introduces a formalism to study non-integrable effects in multi-frequency Sine-Gordon models, highlighting soliton confinement and spectral evolution.

Findings

Non-locality causes soliton confinement in the perturbed theory.

Frequency ratio influences the massless flow and fixed points.

Applications to Ashkin-Teller and Schwinger models demonstrate the formalism's utility.

Abstract

We consider the two-dimensional quantum field theory of a scalar field self-interacting via two periodic terms of frequencies $\alpha$ and $\beta$. Looking at the theory as a perturbed Sine-Gordon model, we use Form Factor Perturbation Theory to analyse the evolution of the spectrum of particle excitations. We show how, within this formalism, the non-locality of the perturbation with respect to the solitons is responsible for their confinement in the perturbed theory. The effects of the frequency ratio $\alpha/\beta$ being a rational or irrational number and the occurrence of massless flows from the gaussian to the Ising fixed point are also discussed. A generalisation of the Ashkin-Teller model and the massive Schwinger model are presented as examples of application of the formalism.