We investigate higher grading integrable generalizations of the affine
Toda systems, where the Bat connections defining the models take valu
es in eigensubspaces of an integral gradation of an affine Kac-Moody a
lgebra, with grades varying from l to -l (l > l). The corresponding ta
rget space possesses nontrivial vacua and soliton configurations, whic
h can be interpreted as particles of the theory, on the same footing a
s those associated to fundamental fields. The models can also be formu
lated by a hamiltonian reduction procedure From the so-called two-loop
WZNW models. We construct the general solution and show the classes c
orresponding to the solitons. Some of the particles and solitons becom
e massive when the conformal symmetry is spontaneously broken by a mec
hanism with an intriguing topological character and leading to a very
simple mass formula, The massive fields associated to nonzero, grade g
enerators obey field equations of the Dirac type and may be regarded a
s matter fields. A special class of models is remarkable. These theori
es possess a U(1) Noether current, which, after a special gauge fixing
of the conformal symmetry, is proportional to a topological current.
This leads to the confinement of the matter field inside the solitons,
which can be regarded as a one-dimensional bag model for QCD. These m
odels are also relevant to the study of electron self-localization in
(quasi-) one-dimensional electron-phonon systems.