Abstract
In the present paper we construct all short representation of so(3, 2) with the sl(2, ℂ) symmetry made manifest due to the use of sl(2, ℂ) spinors. This construction has a natural connection to the spinor-helicity formalism for massless fields in AdS4 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.
Highlights
Construction of interacting theories of massless higher spin fields is a promising, but at the same time a very challenging problem of modern physics
In the present paper we construct all short representation of so(3, 2) with the sl(2, C) symmetry made manifest due to the use of sl(2, C) spinors. This construction has a natural connection to the spinor-helicity formalism for massless fields in AdS4 suggested earlier
In the present paper we will focus on other important representations, relevant for the higher-spin holography — Dirac singletons [55], which are better known as conformal scalar and spinor fields
Summary
Construction of interacting theories of massless higher spin fields is a promising, but at the same time a very challenging problem of modern physics. Whether any holographic construction underlies chiral higher spin theories or not, the manifestly covariant formalism is not suitable for dealing with it as it does not allow to capture all relevant vertices in flat space. In the present paper we will focus on other important representations, relevant for the higher-spin holography — Dirac singletons [55], which are better known as conformal scalar and spinor fields It is worth cautioning the reader, that, while typically the spinor-helicity formalism refers to a more concrete set of techniques that allow to manipulate amplitudes of massless fields in four-dimensional flat space efficiently, in the context of short representations of so(3, 2), we will use this notion more broadly, rather, as a general idea of employing sl(2, C) so(3, 1) spinors to make Lorentz symmetry manifest.
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