Emergent Supersymmetry on the Edges

Abstract

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.

arXiv comment47 pages. We added in the revised manuscript a few paragraphs clarifying the role of fermionization to show emergent supersymmetry of the chiral theory on the edges

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