3d conformal fields with manifest \(sl (2, \mathbb{C} )\)

DOI10.1007/JHEP06(2021)055zbMATH Open1466.81106arXiv2104.02770OpenAlexW3172366603MaRDI QIDQ2044871

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Publication date: 10 August 2021

Published in: (Search for Journal in Brave)

Abstract: In the present paper we construct all short representation of $so(3,2)$ with the $sl(2,mathbbC)$ symmetry made manifest due to the use of $sl(2,mathbbC)$ 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.

Full work available at URL: https://arxiv.org/abs/2104.02770

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