Extended Poincar\'e supersymmetry in three dimensions and supersymmetric anyons

TL;DR

This paper classifies all unitary representations of extended Poincaré supergroups in three dimensions, revealing the existence of supersymmetric anyons with physical momenta and contrasting with the non-supersymmetric case.

Contribution

It provides a complete classification of unitary representations of extended Poincaré supergroups in 3D, including supersymmetric anyons, and shows all have physical momenta.

Findings

Irreducible unitary representations include all spins, representing supersymmetric anyons.

All such representations have physical momenta, unlike the non-supersymmetric case.

Supersymmetry constrains the representations to physically relevant momenta.

Abstract

We classify the unitary representations of the extended Poincar\'e supergroups in three dimensions. Irreducible unitary representations of any spin can appear, which correspond to supersymmetric anyons. Our results also show that all irreducible unitary representations necessarily have physical momenta. This is in sharp contrast to the ordinary Poincar\'e group in three dimensions, that admits in addition irreducible unitary representations with non-physical momenta, which are discarded on physical grounds.