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

We consider a two-dimensional integrable and conformally invariant field th eory possessing two Dirac spinors and three scalar fields. The interaction couples bilinear terms in the spinors to exponentials of the scalars. Its i ntegrability properties are based on the sl(2) affine Kac-Moody algebra, an d it is a simple example of the so-called conformal affine Toda theories co upled to matter fields. We show, using bosonization techniques, that the cl assical equivalence between a U(1)Noether current and the topological curre nt holds true at the quantum level, and then leads to a bag model like mech anism for the confinement of the spinor fields inside the solitons. By boso nizing the spinors we show that the theory decouples into a sine-Gordon mod el and free scalars. We construct the two-soliton solutions and show that t heir 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 th e context of the equivalence between the sine-Gordon and Thirring theories. (C) 2000 Elsevier Science B.V. All rights reserved.