Non-Abelian duality, parafermions, and supersymmetry

Non-Abelian duality in relation to supersymmetry is examined. When the action of the isometry group on the complex structures is nontrivial, extended supersymmetry is realized nonlocally after duality, using path-ordered Wilson lines. Prototype examples considered in detail are, hyper-Kahler metrics with SO(3) isometry and supersymmetric WZW models. For the latter, the natural objects in the nonlocal realizations of supersymmetry arising after duality are the classical non-Abelian parafermions. The canonical equivalence of WZW models and their non-Abelian duals with respect to a vector subgroup is also established. copyright 1996 The American Physical Society