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,~2/3ν=1/2,2/3 are able to support supersymmetry.
Highlights
Introduction and ConclusionEver since its discovery, space-time supersymmetry [1] has been widely utilized in high-energy physics and cosmology
The fractional quantum Hall states are shown to have topological order[8, 9] which is beyond the Landau theory of symmetry breaking
The goal of this paper is to explore the emergent supersymmetry on the edges of the 2 + 1
Summary
Space-time supersymmetry [1] has been widely utilized in high-energy physics and cosmology. A modern understanding of the fermionization is to couple a bosonic theory having non-anomalous 2 symmetry with the low-energy limit of the topological phase of the Kitaev Majorana chain followed by the 2 quotient [22, 20] This idea has been applied in recent works [23, 21, 24, 25, 26, 27]. SUSY conditions that has to be obeyed by any supersymmetric RCFTs. In Sections 3 and 4, we present detailed analyses that show the emergence of supersymmetry for the WZW models in table 1 and 2. In appendix A, we argue that supersymmetry can emerge only for the 6 and 8 parafermion CFTs via the Jordan-Wigner transformation
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