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3d conformal fields with manifest sl(2,mathbb{C})
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3d conformal fields with manifest sl(2,mathbb{C})
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In the present paper we construct all short representation of $so(3,2)$ with the $sl(2,\mathbb{C})$ symmetry made manifest due to the use of $sl(2,\mathbb{C})$ 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.
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