Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State

Abstract

The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured that these modes are superpartners of each other and described by a supersymmetric conformal field theory [1]. We propose a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective spin-3/2 field in the bulk. After breaking supersymmetry through a Goldstino, the spin-3/2 field becomes massive and can be seen as the neutral collective mode that characterizes the Moore-Read state. By integrating out this fermion field, we obtain a purely bosonic topological action that properly encodes the Hall conductivity, Hall viscosity and gravitational anomaly. Our work paves the way to the exploration of the fractional quantum Hall effect through non-relativistic supergeometry.

7 pages, details added, typos corrected

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Cited by in corpus (8)

• Supergravity model of the Haldane-Rezayi fractional quantum Hall state
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• A note on the Hamiltonian structure of transgression forms