On Superconformal Anyons

TL;DR

This paper explores non-relativistic superconformal field theories in 2+1 dimensions describing anyons with unique angular momentum properties, revealing violations of unitarity bounds and analyzing BPS vortices.

Contribution

It introduces a new class of superconformal anyon theories, computes operator dimensions, and constructs a novel supersymmetric gauged linear sigma model for vortex dynamics.

Findings

Chiral primary operators have large anomalous dimensions.

Some operators violate the unitarity bound due to non-normalisable wavefunctions.

BPS vortices emerge at the unitarity bound, with a new sigma model describing their low-energy dynamics.

Abstract

In d=2+1 dimensions, there exist field theories which are non-relativistic and superconformal. These theories describe two species of anyons, whose spins differ by 1/2, interacting in a harmonic trap. We compute the dimensions of chiral primary operators. These operators receive large anomalous dimensions which are related to the unusual angular momentum properties of anyons. Surprisingly, we find that the dimensions of some chiral primary operators violate the unitarity bound and we trace this to the fact that the associated wavefunctions become non-normalisable. We also study BPS non-perturbative states in this theory: these are Jackiw-Pi vortices. We show that these emerge at exactly the point where perturbative operators hit the unitarity bound. To describe the low-energy dynamics of these vortices, we construct a novel type of supersymmetric gauged linear sigma model.