3d conformal fields with manifest sl(2 , ?)

摘要

A bstract In the present paper we construct all short representation of so (3 , 2) with the sl (2 , ?) symmetry made manifest due to the use of sl (2 , ?) spinors. This construction has a natural connection to the spinor-helicity formalism for massless fields in AdS_(4)suggested earlier. We then study unitarity of the resulting representations, identify them as the lowest-weight modules and as conformal fields in the three-dimensional Minkowski space. Finally, we compare these results with the existing literature and discuss the properties of these representations under contraction of so (3 , 2) to the Poincare algebra.