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

TL;DR

This paper develops a non-relativistic supergeometric framework for the Moore-Read fractional quantum Hall state, revealing a massive spin-3/2 mode and deriving a bosonic topological action that captures key physical properties.

Contribution

It introduces a non-relativistic supergeometric theory compatible with the Moore-Read state, linking supersymmetry, bulk modes, and topological responses.

Findings

Identification of a bulk spin-3/2 mode as a neutral collective excitation.

Derivation of a bosonic topological action encoding Hall conductivity and viscosity.

Establishment of a non-relativistic supergeometric approach for fractional quantum Hall systems.

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.