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.

47 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

References in corpus (8)

• Generalized Global Symmetries
• Quantum criticality
• Three-Dimensional Gravity Revisited
• Orbifold groupoids
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Kac-Moody and Virasoro Characters from the Perturbative Chern-Simons Path Integral
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Quantum Criticality in Topological Insulators and Superconductors: Emergence of Strongly Coupled Majoranas and Supersymmetry

Cited by in corpus (2)

• Bootstrapping Fermionic Rational CFTs with Three Characters
• Engineering of Anyons on M5-Probes via Flux Quantization