Quasiparticle spin from adiabatic transport in quantum Hall trial wavefunctions

Understand

Quasiparticle spin (in the spacetime sense) couples to curvature of space.

• Here this fact is used to calculate the spin of quasiholes in trial quantum Hall states by adiabatically dragging them around on a sphere, for trial states given by conformal blocks in some conformal field theory.
• The spin is found to agree with the conformal weight of the corresponding field.
• The result completes a recent argument that constructions using blocks from non-unitary theories that contain negative quantum dimensions produce contradictions that prevent them from describing topological (gapped) phases of matter.