Generalised superconformal higher-spin multiplets

Kuzenko, Sergei M.; Ponds, Michael; Raptakis, Emmanouil S. N.

doi:10.1007/jhep03(2021)183

“…Interestingly, the higher-depth gauge transformations (4.18a) are different to those proposed for the generalised superconformal multiplets in[73]. The latter transformations possess the same functional form as the second group of terms in(3.46).…”

mentioning

confidence: 80%

AdS superprojectors

Buchbinder

¹

,

Hutchings

²

,

Kuzenko

³

et al. 2021

J. High Energ. Phys.

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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.

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“…In all, even though the program of constructing CHS gauge fields in a curve background is far from being settled, even for the spin-3, we expect that once the mixing issue is resolved a proper holographic picture will come up for free fields and our present results, although somewhat preliminary, will prove useful in that endeavour. Let us close by mentioning an interesting approach to bypass the problem of factorization and further study the mixing of CHS that has been recently proposed in [28]. This shifts the focus to maximal depth CHS fields and decreases the order of the kinetic operator.…”

Section: Jhep05(2021)241mentioning

confidence: 99%

A calculation of the Weyl anomaly for 6D conformal higher spins

Aros

¹

,

Bugini

²

,

Díaz

³

2021

J. High Energ. Phys.

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In this work we continue the study of the one-loop partition function for higher derivative conformal higher spin (CHS) fields in six dimensions and its holographic counterpart given by massless higher spin Fronsdal fields in seven dimensions.In going beyond the conformal class of the boundary round 6-sphere, we start by considering a Ricci-flat, but not conformally flat, boundary and the corresponding Poincaré-Einstein space-filling metric. Here we are able to match the UV logarithmic divergence of the boundary with the IR logarithmic divergence of the bulk, very much like in the known 4D/5D setting, under the assumptions of factorization of the higher derivative CHS kinetic operator and WKB-exactness of the heat kernel of the dual bulk field. A key technical ingredient in this construction is the determination of the fourth heat kernel coefficient b6 for Lichnerowicz Laplacians on both 6D and 7D Einstein manifolds. These results allow to obtain, in addition to the already known type-A Weyl anomaly, two of the three independent type-B anomaly coefficients in terms of the third, say c3 for instance.In order to gain access to c3, and thus determine the four central charges independently, we further consider a generic non Ricci-flat Einstein boundary. However, in this case we find a mismatch between boundary and bulk computations for spins higher than two. We close by discussing the nature of this discrepancy and perspectives for a possible amendment.

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“…For further details regarding their dual gauge prepotentials and the superconformal field theories they induce, we refer the reader to [3][4][5][6]. See also [7] for their higher-depth generalisations.…”

Section: Reduction To N = 1 Superspacementioning

confidence: 99%

“…which holds up to a total derivative. 7 For simplicity, we do not include any numerical factors in (4.18) and (4.19).…”

Section: Superconformal Gauge-invariant Modelsmentioning

confidence: 99%

“…In four dimensions, off-shell N = 1 superconformal higher-spin prepotentials were briefly discussed by Howe, Stelle and Townsend in the framework of supercurrent multiplets in 1981 [1], a few years before Fradkin and Tseytlin [2] constructed the free conformal higherspin actions in Minkowski space. It was only in the last few years that these prepotentials and more general off-shell gauge supermultiplets were finally used to construct free N = 1 superconformal higher-spin gauge theories in Minkowski space [3] and arbitrary conformally flat and Bach flat backgrounds [4][5][6][7]. Parallel studies in three dimensions (3D) to describe superconformal higher-spin multiplets and the corresponding Chern-Simons actions were conducted [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Extended superconformal higher-spin gauge theories in four dimensions

Kuzenko

¹

,

Raptakis

²

2021

J. High Energ. Phys.

Self Cite

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Using the off-shell formulation for $$ \mathcal{N} $$ N = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main $$ \mathcal{N} $$ N = 2 results are then generalised to the $$ \mathcal{N} $$ N -extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin $$ \mathcal{N} $$ N = 2 supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the $$ \mathcal{N} $$ N = 2 superconformal group.

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Generalised superconformal higher-spin multiplets

Abstract: We propose generalised $$ \mathcal{N} $$ N = 1 superconformal higher-spin (SCHS) gauge multiplets of depth t, $$ {\Upsilon}_{\alpha (n)\overset{\cdot }{\alpha }(m)}^{(t)} $$ ϒ α n α ⋅ m … Show more

Cited by 7 publications

References 156 publications

AdS superprojectors

AdS superprojectors

A calculation of the Weyl anomaly for 6D conformal higher spins

Extended superconformal higher-spin gauge theories in four dimensions

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