  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.
