Abstract
We elaborate on the traceless and transverse spin projectors in four-dimensional de Sitter and anti-de Sitter spaces. The poles of these projectors are shown to correspond to partially massless fields. We also obtain a factorisation of the conformal operators associated with gauge fields of arbitrary Lorentz type (m/2,n/2), with m and n positive integers.
Highlights
In four-dimensional Minkowski space M4, spin projection operators, known as traceless and transverse (TT) spin-s projectors, were constructed by Behrends and Fronsdal more than sixty years ago [1, 2]
An important example of the latter application is the formulation of conformal higher-spin actions proposed by Fradkin and Tseytlin [3], the TT spin-s projectors were given explicitly in [3] only for s ≤ 2
Refs. [1, 2] made use of the four-vector notation in conjunction with the four-component spinor formalism, which resulted in rather complicated expressions for the TT spin-s projectors
Summary
In four-dimensional Minkowski space M4, spin projection operators, known as traceless and transverse (TT) spin-s projectors, were constructed by Behrends and Fronsdal more than sixty years ago [1, 2]. These TT projectors have found numerous applications. Unlike Minkowski space, both de Sitter (dS) and anti-de Sitter (AdS) spaces have nonvanishing curvature, which makes it more challenging to construct the TT spin-s projectors For this reason only the lower-spin cases corresponding to s ≤ 2 have been considered in the literature [13]. An analysis similar to that given below applies in the case of de Sitter space, one just needs to replace all occurrences of S2 with −S2
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