The sl(2) affine Toda model coupled to the matter: solitons and confinement

The so-called conformal affine Toda theory coupled to the matter fields (CATM), associated to the sl(2) affine Lie algebra, is studied. The conformal symmetry is fixed by setting a connection to zero, then one defines an off-critical model, the affine Toda model coupled to the matter (ATM). Using the 'dressing' transformation method we construct the explicit forms of the two-soliton classical solutions, and show that a physical bound soliton-anti soliton pair (breather) does not exist. Moreover, we verify that these solutions share some features of the sine-Gordon (massive Thirring) solitons, and satisfy the classical equivalence of topological and Noether currents in the ATM model. We show, using bosonization techniques that the Noether and topological currents equivalence as a constraint, one can show that the ATM model leads to a bag model like mechanism for the confinement of the 'color' charge inside the sine-Gordon solitons (baryons). (author)