Kac-Moody construction of Toda type field theories

Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

“…For the principal gradation, we recover the abelian CAT model of [6,7], and we show that the Hirota's τ -functions defined in [9,31] easily follow from the systematic approach of section 8. For the homogeneous gradation, we construct the one-soliton solutions when the finite Lie algebra G is either compact or non-compact; in the former case, the resulting model has very suggestive features.…”

“…The two-loop WZNW model was introduced in [6] as the generalization of the ordinary WZNW model to the affine case. Its equations of motion are given by…”

“…Finally, the conformal symmetry can be restored in the abelian Affine Toda models just by adding two extra fields which do not modify the dynamics of the original model; one of these fields is a connection whose only role is to implement the conformal invariance. These are the so called Conformal Affine Toda models [6,7], and they are based on a full Kac-Moody algebra; moreover, they are integrable [8], and have soliton solutions [9]. In fact, many properties of the Affine Toda models can be more easily understood by considering them as the Conformal Affine Toda models with the conformal symmetry spontaneously broken.…”

“…In fact, many properties of the Affine Toda models can be more easily understood by considering them as the Conformal Affine Toda models with the conformal symmetry spontaneously broken. All these Toda models can be obtained via Hamiltonian reductions of WZNW models [10,6],whilst their one dimensional versions can be obtained from free motion on symmetric spaces [11,12].…”

“…Notice that we allow the central term ofĜ and the grading operator to be generators of G 0 ; this leads to the conformal invariance of the G-CAT models, which generalizes the CAT models [6,7] for non-abelian groups.…”