THE WZW MODEL AS A DYNAMICAL SYSTEM ON AFFINE LIE-GROUPS

Working directly on affine Lie groups, we construct several new formul ations of the WZW model. In one formulation WZW is expressed as a one- dimensional mechanical system whose variables are coordinates on the a ffine Lie group. When written in terms of the affine group element, th is formulation exhibits a two-dimensional WZW term. In another formula tion WZW is written as a two-dimensional field theory, with a three-di mensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translatio n dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional WZW formulation o n the Lie group. Using this dictionary, we also express WZW as a three -dimensional field theory on the Lie group with a four-dimensional WZW term.