Weyl action of two-column mixed-symmetry field and its factorization around (A)dS space

Abstract

Abstract:We investigate the four-derivative free Weyl action for two-column mixedsymmetry field that makes use of maximal gauge symmetries. In flat space, the action can be uniquely determined from gauge and Weyl (trace shift) symmetry requirements. We show that there is a smooth and unique deformation of the flat action to (A)dS which keeps the same amount of gauge symmetries. This action admits a factorization into two distinct two-derivative actions having gauge parameters of different Young diagrams. Hence, this factorization pattern naturally extends that of the Weyl actions of symmetric higher spin fields to mixed-symmetry cases. The mass-deformation for these actions can be realized preserving one of the gauge symmetries. Although generically non-unitary, in special dimensions, unitarity is achieved selecting different mass deformations for dS and AdS. We consider particular examples of our construction such as New Massive Gravity in three dimensions, linearized bigravity in four dimensions and their arbitrary dimensional generalizations.

Spin projection operators in (A)dS and partial masslessness

“…For lower-spin values s = 3/2 and s = 2, corresponding to m = n − 1 = 1 and m = n = 2 respectively, the factorisation of the conformal operators (3.12) was observed long ago in [14,29,30]. This factorisation was conjectured, based on lower-spin examples, by Tseytlin [31] for the bosonic m = n and fermionic m = n − 1 cases, and also by Joung and Mkrtchyan [32,33] for certain bosonic CHS models. More recently, the factorisation was proved by several groups [28,34,35] for those bosonic CHS models on AdS d , with even d, which are described by completely symmetric arbitrary spin conformal fields (the m = n case in four dimensions).…”

Dual actions for massless, partially-massless and massive gravitons in (A)dS

“…In this case, in the limit λ → 0 the field T decomposes into a "proper" [n−3, 1] dual graviton plus an additional field of type [n − 2, 1] that does not carry any local degrees of freedom. See [10,43] for further comments on the role of the field T . This phenomenon can be described by introducing a suitable set of Stueckelberg fields.…”

Conformal higher spin scattering amplitudes from twistor space

“…The generating functional is quadratic in the negative helicity CHS states, defined on a non-linear, Bach-flat (in particular, self-dual) spin-two background. It is therefore natural to conjecture that (3.2) is equivalent to the SD part of quadratic covariant action for CHS fields on a conformal gravity background, whose existence was argued in [39] (see also [40] and [41,42]). We hope to investigate this further in the future.…”