Emergent Supersymmetry on the Edges

TL;DR

This paper investigates the conditions under which WZW models, describing edge modes of Chern-Simons theories, can exhibit emergent supersymmetry, including cases with spontaneous supersymmetry breaking and potential links to quantum Hall states.

Contribution

It demonstrates how certain WZW models can be mapped to supersymmetric theories and discusses the presence or absence of supersymmetry in these models, including implications for quantum Hall states.

Findings

Some WZW models have supersymmetric Ramond vacua.

Others exhibit spontaneous supersymmetry breaking.

Potential support for supersymmetry in Read-Rezayi states at specific filling fractions.

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.