Formal Higher Spin Gravities

Sharapov, A. A.; Skvortsov, Evgeny

doi:10.1016/j.nuclphysb.2019.02.011

Cited by 29 publications

(41 citation statements)

References 85 publications

(204 reference statements)

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“…There is also a simple differential equation that allows one to generate the vertices V n and to prove their formal consistency [41,44,59]. Thus, we see that the vertices are completely determined by the associative •-product (3.3).…”

Section: B)mentioning

confidence: 92%

“…12 Intuitively, it is clear that the higher spin algebra hs (together with π) is the only input data for the problem and the interaction vertices V n , n > 2, should be derivable from it. The precise relation between hs and V n 's for any hs was established in [41,44].…”

Section: B)mentioning

confidence: 99%

“…The main statement of [41] is that (up to formal field re-definitions) the nontrivial interaction vertices are in one-to-one correspondence with the nontrivial deformations of π hs as an associative algebra. The deformation of an associative algebra π hs appears to be a much simpler problem to solve.…”

Section: B)mentioning

confidence: 99%

“…In Section 2, we review various definitions of the 5d higher spin algebra and discuss the free equations, i.e., up to V 2 in (1.1). In Section 3, we summarize the central result of [41] that simplifies the problem. The main results of the present paper are in Section 4, where we formulate two different ways to describe the deformed higher spin algebra.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Towards massless sector of tensionless strings on AdS5

2020

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A Formal Higher Spin Gravity in five dimensions is constructed. It was shown recently that constructing formally consistent classical equations of motion of higher spin gravities is equivalent to finding a certain deformation of a given higher spin algebra. A strong homotopy algebra encoding the interaction vertices then follows.We propose two different and novel realizations of the deformed higher spin algebra in the case of five dimensions: one in terms of the universal enveloping algebra of su(2, 2) and the other by means of oscillator variables. Both the new realizations are amenable to supersymmetric extensions and the N = 8 case underlies the massless sector of tensionless strings.

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Section: B)mentioning

confidence: 92%

Section: B)mentioning

confidence: 99%

Section: B)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards massless sector of tensionless strings on AdS5

2020

Self Cite

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“…• In this paper we only started to explore the interactions in the bulk theory following from making the theory higher-spin gauge invariant; of course this is not expected to be the full story and it would be very interesting to get a handle on further interactions. Here, one should distinguish between to types: firstly, there could be interactions coming from 'formal' deformations of the higher spin algebra [63]. In the case of higher spin theories with hs[λ] gauge symmetry these were argued to be absent; it is not known whether this result persists for the higher spin square.…”

Section: Supermultiplet Spectrummentioning

confidence: 99%

On tensionless string field theory in AdS3

Raeymaekers

2019

J. High Energ. Phys.

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We report on progress in formulating a field theory of tensionless strings in AdS 3 , starting from the dual large-N symmetric orbifold CFT. We propose a set of field equations which are gauge invariant under the higher spin algebra of the theory, the 'Higher Spin Square'. The massless higher spin sector is captured by a Chern-Simons gauge field, while the matter sector is described by unfolded equations similar to those appearing in Vasiliev theory. Our equations incorporate the full perturbative spectrum of the theory, including states coming from the twisted sectors, and capture some of the interactions fixed by gauge invariance. We also discuss the spectrum of the bulk theory and explain how linearization around AdS 3 gives rise to the expected set of decoupled wave equations. Our results can be generalized to describe bulk duals of other large-N symmetric orbifolds. arXiv:1903.09647v2 [hep-th] 4 Apr 2019 30 5.4 Tensionless string field equations 33 5.5 Spectrum and supermultiplet decomposition 35 6 Outlook 38

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Towards higher-spin AdS2/CFT1 holography

Alkalaev

Bekaert

2020

J. High Energ. Phys.

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We aim at formulating a higher-spin gravity theory around AdS 2 relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins of the standard higher-dimensional structures in higher-spin gravity such as the singleton, the higher-spin symmetry algebra, the higher-rank gauge and matter fields, etc. In particular, the higher-spin algebra is given here by hs[λ] and parameterized by a real parameter λ. The singleton is defined to be a Verma module of the AdS 2 isometry subalgebra so(2, 1) ⊂ hs[λ] with conformal weight ∆ = 1±λ2 . On the one hand, the spectrum of local modes is determined by the Flato-Fronsdal theorem for the tensor product of two such singletons. It is given by an infinite tower of massive scalar fields in AdS 2 with ascending masses expressed in terms of λ. On the other hand, the higher-spin fields arising through the gauging of hs[λ] algebra do not propagate local degrees of freedom. Our analysis of the spectrum suggests that AdS 2 higher-spin gravity is a theory of an infinite collection of massive scalars with fine-tuned masses, interacting with infinitely many topological gauge fields. Finally, we discuss the holographic CFT 1 duals of the kinematical structures identified in the bulk.

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Formal Higher Spin Gravities

Cited by 29 publications

References 85 publications

Towards massless sector of tensionless strings on AdS5

Towards massless sector of tensionless strings on AdS5

On tensionless string field theory in AdS3

Towards higher-spin AdS2/CFT1 holography

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