Long, partial-short, and special conformal fields

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.

Section: Identification As Conformal Fieldsmentioning

confidence: 94%

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

Ponomarev

2021

“…To see that it is nevertheless the case let us denote Ψ = B ℓ−1 k Φ, Ψ ∈ S[s, 1 − 1 2 n]. The equation B t Ψ = 0, t = s − 2 + n 2 can be regarded in n = 4 as a maximal depth CHS equations while in n > 4 as a so-called "long" CHS fields [45]. Let us now find find…”

Section: Proof Of Proposition 33mentioning

confidence: 99%

On the structure of the conformal higher-spin wave operators

Grigoriev

Hancharuk

2018

We study conformal higher spin (CHS) fields on constant curvature backgrounds. By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin s and gauge invariance of arbitrary order t s. In the case of the usual Fradkin-Tseytlin fields t = 1 this gives a systematic derivation of the factorization formulas known in the literature while for t > 1 the explicit formulas were not known. We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries.

“…We note that the ordinary-derivative formulation of conformal fields in refs. [68,69] and Stueckelberg formulation of massive fields share some common features. The light-cone gauge approach considerably simplifies the investigation of interacting massive fields.…”

Section: Jhep12(2021)069mentioning

confidence: 99%

Superfield approach to interacting N = 2 massive and massless supermultiplets in 3d flat space

Metsaev

2021

Self Cite

Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N = 2 Poincaré superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are studied. For such massive and massless supermultiplets, a formulation in terms of light-cone gauge unconstrained superfields defined in a momentum superspace is developed. For the supermultiplets under consideration a superspace first derivative representation for all cubic interaction vertices is obtained. A superspace representation for dynamical generators of the N = 2 Poincaré superalgebra is also found.