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

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.Comment: 7 pages; commentaries added in Sect. IV A and in Conclusion; added reference