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

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 boson and a chiral Majorana mode on the boundary. It has been recently conjectured that these two boundary modes are superpartners of each other and described by a supersymmetric conformal field theory.

In this talk, we present a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective gravitino in the bulk. After breaking supersymmetry through a goldstino (i.e. a Nambu-Goldstone fermion), the gravitino becomes massive and can be seen as the neutral spin-3/2 collective mode that characterizes the Moore-Read state in the bulk. After integrating out this fermion field, we obtain a purely bosonic topological action that properly encodes the Hall conductivity, Hall viscosity and gravitational anomaly.