Noether and topological currents equivalence and soliton/particle correspondence in affine sl(2)((1)) Toda theory coupled to matter

A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivalence between the Noether and topological currents. The classical solitonic spectrum of the ATM model is also discussed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

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 (s) over capl(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-antisoliton 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 ATM theory decouples into a sine-Gordon model and a free scalar. Imposing 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).

The Faddeev-Jackiw approach and the conformal affine sl(2) Toda model coupled to the matter field

The conformal affine sl(2) Toda model coupled to the matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either the sine-Gordon or the massive Thirring model, through a process of Hamiltonian reduction, considering the equivalence of the Noether and topological currrents as a constraint and gauge fixing the conformal symmetry. (C) 2000 Academic Press.

A Bethe ansatz solution for the closed U-q[sl(2)] Temperley-Lieb quantum spin chains

We solve the spectrum of the closed Temperley-Lieb quantum spin chains using the coordinate Bethe ansatz. These models are invariant under the quantum group U-q[sl(2)].

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.