Spin projection operators in (A)dS and partial masslessness

Self Cite

In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor ℭα(n)(h) is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential hα(n). The explicit form of ℭα(n)(h) is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for ℭα(n)(h) in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action $$ {S}_{\mathrm{CS}}^{(n)}\left[h\right]\propto \int {\mathrm{d}}^3{xeh}^{\alpha (n)}{\mathrm{\mathfrak{C}}}_{\alpha (n)}(h) $$ S CS n h ∝ ∫ d 3 xeh α n ℭ α n h factorises into a product of (n − 1) first-order operators that are associated with the spin-n/2 partially massless AdS values. Our findings greatly facilitate the on-shell analysis of massive higher-spin gauge-invariant actions in AdS3. The main results are extended to the case of $$ \mathcal{N} $$ N = 1 AdS supersymmetry. In particular, we derive simple expressions for the higher-spin super-Cotton tensors in AdS3.

Section: Discussionsupporting

confidence: 93%

Section: Discussionmentioning

confidence: 99%

Higher-spin Cotton tensors and massive gauge-invariant actions in AdS3

Kuzenko

Ponds

2021

Self Cite

“…Irreducible supermultiplets of the types (1.5), (1.6) and (1.7) have been used in [28] for the covariant quantisation of the massless supersymmetric higher-spin gauge theories in AdS 4 [16]. The Behrends-Fronsdal projectors have been generalised to the case of AdS 4 only recently in [29]. One of the important outcomes of [29] was a new understanding of the so-called partially massless fields in AdS 4 .…”

Section: B)mentioning

confidence: 99%

“…The Behrends-Fronsdal projectors have been generalised to the case of AdS 4 only recently in [29]. One of the important outcomes of [29] was a new understanding of the so-called partially massless fields in AdS 4 . Such fields in diverse dimensions were studied earlier in [30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Section: B)mentioning

confidence: 99%

“…Such fields in diverse dimensions were studied earlier in [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Specifically, it was shown in [29] that the partially massless fields are associated with the poles of the spin projection operators in AdS 4 . In the present paper we provide an N = 1 supersymmetric extension of the AdS 4 spin projection operators JHEP04(2021)074 and describe various applications of the resulting superprojectors.…”

Section: B)mentioning

confidence: 99%

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AdS superprojectors

Buchbinder

Hutchings

Kuzenko

et al. 2021

Within the framework of $$ \mathcal{N} $$ N = 1 anti-de Sitter (AdS) supersymmetry in four dimensions, we derive superspin projection operators (or superprojectors). For a tensor superfield $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)}:= {\mathfrak{V}}_{\left(\alpha 1\dots \alpha m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ V α m α ⋅ n ≔ V α 1 … αm α ⋅ 1 … α ⋅ n on AdS superspace, with m and n non-negative integers, the corresponding superprojector turns $$ {\mathfrak{V}}_{\alpha (m)\overset{\cdot }{\alpha }(n)} $$ V α m α ⋅ n into a multiplet with the properties of a conserved conformal supercurrent. It is demonstrated that the poles of such superprojectors correspond to (partially) massless multiplets, and the associated gauge transformations are derived. We give a systematic discussion of how to realise the unitary and the partially massless representations of the $$ \mathcal{N} $$ N = 1 AdS4 superalgebra $$ \mathfrak{osp} $$ osp (1|4) in terms of on-shell superfields. As an example, we present an off-shell model for the massive gravitino multiplet in AdS4. We also prove that the gauge-invariant actions for superconformal higher-spin multiplets factorise into products of minimal second-order differential operators.

Spin-(s, j) projectors and gauge-invariant spin-s actions in maximally symmetric backgrounds

Hutchings,

Ponds

2024

Given a maximally symmetric d-dimensional background with isometry algebra $$ \mathfrak{g} $$ g , a symmetric and traceless rank-s field ϕa(s) satisfying the massive Klein-Gordon equation furnishes a collection of massive $$ \mathfrak{g} $$ g -representations with spins j ∈ {0, 1, · · · , s}. In this paper we construct the spin-(s, j) projectors, which are operators that isolate the part of ϕa(s) that furnishes the representation from this collection carrying spin j. In the case of an (anti-)de Sitter ((A)dSd) background, we find that the poles of the projectors encode information about (partially-)massless representations, in agreement with observations made earlier in d = 3, 4. We then use these projectors to facilitate a systematic derivation of two-derivative actions with a propagating massless spin-s mode. In addition to reproducing the massless spin-s Fronsdal action, this analysis generates new actions possessing higher-depth gauge symmetry. In (A)dSd we also derive the action for a partially-massless spin-s depth-t field with 1 ≤ t ≤ s. The latter utilises the minimum number of auxiliary fields, and corresponds to the action originally proposed by Zinoviev after gauging away all Stückelberg fields. Some higher-derivative actions are also presented, and in d = 3 are used to construct (i) generalised higher-spin Cotton tensors in (A)dS3; and (ii) topologically-massive actions with higher-depth gauge symmetry. Finally, in four-dimensional $$ \mathcal{N} $$ N = 1 Minkowski superspace, we provide closed-form expressions for the analogous superprojectors.