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

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.

Carrollian and Galilean conformal higher-spin algebras in any dimensions

“…We verify in appendix C.1 that these relations span an ideal, that we denote by I c . Notice that we recovered the condition P a P b ∼ 0 that was already manifest in D = 3 and that emerged in the flat limit of the scalar singleton in D = 4 proposed in [122]. On the other hand, we do not have to impose the stronger constraint P a ∼ 0 that characterises the flat limit proposed in [123].…”

“…Furthermore, the ideal to be factored out from U (so(2, D − 1)) to get hs D corresponds to the annihilator of the scalar singleton module: our procedure thus defines implicitly both an ultra-and a non-relativistic limit of the scalar singleton. In particular, let us remind that the contraction to Poincaré leads to an ideal including the condition P a P b ∼ 0, which also independently emerged in the study of the flat limit of the scalar singleton in [122], but which is weaker than the trivial action of translations that characterise the flat limit proposed in [123].…”

Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes

“…In this regard, we would like to mention, that just the Killing tensors, transforming in the appropriate representations of the Poincare algebra can already be regarded as the flat-space higher-spin algebra. Some more non-trivial examples of flat-space higher-spin algebras were constructed recently as the result of contraction of the AdS higher-spin algebra [58], while the associated singleton representation in the 4d case was constructed in [59]. A somewhat unattractive feature of this latter algebra is that parameters of higher-spin symmetries do not transform as Killing tensors under the Poincare algebra.…”

Invariant traces of the flat space chiral higher-spin algebra as scattering amplitudes

“…In this regard, we would like to mention, that just the Killing tensors, transforming in the appropriate representations of the Poincare algebra can already be regarded as the flat-space higher-spin algebra. Some more non-trivial examples of flat-space higher-spin algebras were constructed recently as the result of contraction of the AdS higher-spin algebra [51], while the associated singleton representation in the 4d case was constructed in [52]. A somewhat unattractive feature of this latter algebra is that parameters of higher-spin symmetries do not transform as Killing tensors under the Poincare algebra.…”