Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models

TL;DR

This paper explores a two-dimensional integrable field theory demonstrating the quantum equivalence between a coupled scalar-spinor model and the sine-Gordon model, providing insights into soliton confinement and duality with the Thirring model.

Contribution

It establishes the quantum equivalence of a conformal affine Toda theory with the sine-Gordon model and elucidates soliton confinement mechanisms.

Findings

Quantum equivalence between the model and sine-Gordon theory confirmed.

Soliton interactions produce time delays consistent with sine-Gordon solitons.

Bosonization reveals decoupling into sine-Gordon and free scalar fields.

Abstract

We consider a two-dimensional integrable and conformally invariant field theory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its integrability properties are based on the sl(2) affine Kac-Moody algebra, and it is a simple example of the so-called conformal affine Toda theories coupled to matter fields. We show, using bosonization techniques, that the classical equivalence between a U(1) Noether current and the topological current holds true at the quantum level, and then leads to a bag model like mechanism for the confinement of the spinor fields inside the solitons. By bosonizing the spinors we show that the theory decouples into a sine-Gordon model and free scalars. We construct the two-soliton solutions and show that their interactions lead to the same time delays as those for the sine-Gordon solitons. The model provides a good laboratory to test duality ideas in the context of the equivalence between the sine-Gordon and Thirring theories.