  The WZW models describe the dynamics of the edge modes of Chern-Simons
theories in three dimensions. We explore the WZW models which can be mapped to
supersymmetric theories via the generalized Jordan-Wigner transformation. Some
of such models have supersymmetric Ramond vacua, but the others break the
supersymmetry spontaneously. We also make a comment on recent proposals that
the Read-Rezayi states at filling fraction $\nu=1/2,~2/3$ are able to support
supersymmetry.
