No abstract

We investigate higher grading integrable generalizations of the affine Toda systems, where the flat connections defining the models take values in eigensubspaces of an integral gradation of an affine Kac-Moody algebra, with grades varying from l to −l (l > 1). The corresponding target space possesses nontrivial vacua and soliton configurations, which can be interpreted as particles of the theory, on the same footing as those associated to fundamental fields. The models can also be formulated by a Hamiltonian reduction procedure from the so called two-loop WZNW models. We construct the general solution and show the classes corresponding to the solitons. Some of the particles and solitons become massive when the conformal symmetry is spontaneously broken by a mechanism with an intriguing topological character and leading to a very simple mass formula. The massive fields associated to non zero grade generators obey field equations of the Dirac type and may be regarded as matter fields. A special class of models is remarkable. These theories 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 models are also relevent to the study of electron self-localization in (quasi)-one-dimensional electron-phonon systems.

No abstract

Non-abelian Toda theories are shown to provide exactly solvable conformal systems in the presence of a black hole. They correspond to gauged WZNW models where the gauge group is nilpotent, and are thus basically different from the ones currently considered, following Witten. The non-abelian Toda potential gives a cosmological term which may be integrated exactly at the classical level.