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Journal ArticleDOI

Non-abelian cubic vertices for higher-spin fields in AdS(d)

03 May 2013-Journal of High Energy Physics (Società italiana di fisica)-Vol. 2013, Iss: 05, pp 8
TL;DR: In this article, the Fradkin-Vasiliev procedure was used to construct the full set of non-Abelian cubic vertices for totally symmetric higher spin gauge fields in AdS d in flat space.
Abstract: We use the Fradkin-Vasiliev procedure to construct the full set of non-Abelian cubic vertices for totally symmetric higher spin gauge fields in AdS d space. The number of such vertices is given by a certain tensor-product multiplicity. We discuss the one-to-one relation between our result and the list of non-Abelian gauge deformations in flat space obtained elsewhere via the cohomological approach. We comment about the uniqueness of Vasiliev’s simplest higher-spin algebra in relation with the (non)associativity properties of the gauge algebras that we classified. The gravitational interactions for (partially)-massless (mixed)-symmetry fields are also discussed. We also argue that those mixed-symmetry and/or partially-massless fields that are described by one-form connections within the frame-like approach can have non-Abelian interactions among themselves and again the number of non-Abelian vertices should be given by tensor product multiplicities.

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Citations
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Journal ArticleDOI
TL;DR: In this paper, the quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of previous results for the Witten diagrams of higher-spin exchanges.
Abstract: Clarifying the locality properties of higher-spin gravity is a pressing task, but notoriously difficult due to the absence of a weakly-coupled flat regime. The simplest non-trivial case where this question can be addressed is the quartic self-interaction of the AdS scalar field present in the higher-spin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higher-spin theory on AdS4 and the free O(N) vector model in three dimensions. In particular, we determine the exact explicit form of the derivative expansion of the bulk scalar quartic vertex. The quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higher-spin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary four-point function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.

220 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the uniqueness of higher-spin algebras and showed that the Eastwood-Vasiliev algebra is the unique solution for d = 4 and d > 7.
Abstract: We study the uniqueness of higher-spin algebras which are at the core of higher-spin theories in AdS and of CFTs with exact higher-spin symmetry, i.e. conserved tensors of rank greater than two. The Jacobi identity for the gauge algebra is the simplest consistency test that appears at the quartic order for a gauge theory. Similarly, the algebra of charges in a CFT must also obey the Jacobi identity. These algebras are essentially the same. Solving the Jacobi identity under some simplifying assumptions spelled out, we obtain that the Eastwood-Vasiliev algebra is the unique solution for d = 4 and d > 7. In 5d there is a one-parameter family of algebras that was known before. In particular, we show that the introduction of a single higher-spin gauge field/current automatically requires the infinite tower of higher-spin gauge fields/currents. The result implies that from all the admissible non-Abelian cubic vertices in AdSd, that have been recently classified for totally symmetric higher-spin gauge fields, only one vertex can pass the Jacobi consistency test. This cubic vertex is associated with a gauge deformation that is the germ of the Eastwood-Vasiliev’s higher-spin algebra.

168 citations

Journal ArticleDOI
TL;DR: In this paper, a fully-gauge and o(d, 2 ) -covariant approach to boundary values of AdS d + 1 gauge fields is presented.

161 citations

Journal ArticleDOI
TL;DR: In this article, the authors compute the complete bulk-to-bulk propagators for massless bosonic higher-spin fields in the metric-like formulation, in any dimension and in various gauges.
Abstract: Within holography, we calculate the contribution of an arbitrary spin-s gauge boson exchange in AdS d+1 to the four-point function with scalar operators on the boundary. As an important ingredient, we first compute the complete bulk-to-bulk propagators for massless bosonic higher-spin fields in the metric-like formulation, in any dimension and in various gauges. The split representation of the bulk-to-bulk propagators in terms of bulk-to-boundary propagators allows to present the higher-spin exchange diagram in the form of a conformal partial wave expansion. Our results provide a step towards the larger goal of the holographic reconstruction of bulk interactions, and of clarifying bulk locality.

143 citations

Journal ArticleDOI
TL;DR: In this paper, the authors make an explicit link between the cubic interactions of off-shell fields and the on-shell three-point amplitudes in four dimensions, and derive the covariant form of all parity-odd massless vertices.
Abstract: We make an explicit link between the cubic interactions of off-shell fields and the on-shell three-point amplitudes in four dimensions. Both the cubic interactions and the on-shell three-point amplitudes had been independently classified in the literature, but their relation has not been made explicit. The aim of this note is to provide such a relation and discuss similarities and differences of their constructions. For the completeness of our analysis, we also derive the covariant form of all parity-odd massless vertices.

111 citations

References
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Journal ArticleDOI
TL;DR: In this article, the authors analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p > 1.
Abstract: Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p > 1. Under the assumptions of locality and Poincare invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term. © SISSA/ISAS 2004.

44 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider a special class of AdS d mixed-symmetry bosonic massless fields corresponding to arbitrary two-column Young tableaux and find unique gauge-invariant free actions and analyze the equations of motion.
Abstract: We consider a particular class of AdS d mixed-symmetry bosonic massless fields corresponding to arbitrary two-column Young tableaux. We find unique gauge-invariant free actions and analyze the equations of motion.

43 citations

Book ChapterDOI
TL;DR: In this article, the lowest eigenvalues of the energy operator for the massless fields and the gauge parameter fields are derived in SO(d−1,2) covariant form as well as in terms of intrinsic coordinates.
Abstract: Arbitrary spin free massless bosonic fields propagating in even d — dimensional anti-de Sitter spacetime are investigated. Free wave equations of motion, subsidiary conditions and the corresponding gauge transformations for such fields are proposed. The lowest eigenvalues of the energy operator for the massless fields and the gauge parameter fields are derived. The results are formulated in SO(d−1,2) covariant form as well as in terms of intrinsic coordinates. An interrelation of two definitions of masslessness based on gauge invariance and conformal invariance is discussed.

40 citations

Journal ArticleDOI
TL;DR: Using frame-like gauge invariant formulation, this paper extended Fradkin-Vasiliev procedure for investigation of gravitational interactions for massless particles in AdS space, to the case of electromagnetic interactions for massive particles leaving in (A)dS space with arbitrary value of cosmological constant including flat Minkowski space.
Abstract: In this paper we investigate electromagnetic interactions for simplest massive mixed symmetry field. Using frame-like gauge invariant formulation we extend Fradkin-Vasiliev procedure, initially proposed for investigation of gravitational interactions for massless particles in AdS space, to the case of electromagnetic interactions for massive particles leaving in (A)dS space with arbitrary value of cosmological constant including flat Minkowski space. At first, as an illustration of general procedure, we re-derive our previous results on massive spin 2 electromagnetic interactions and then we apply this procedure to massive mixed symmetry field. These two cases are just the simplest representatives of two general class of fields, namely completely symmetric and mixed symmetry ones, and it is clear that the results obtained admit straightforward generalization to higher spins as well.

40 citations

Journal ArticleDOI
TL;DR: In this paper, a Fradkin-Vasiliev approach was used to construct cubic gravitational interactions for a massless mixed symmetry field in an AdS space with arbitrary values of the cosmological constant including a flat Minkowski space.
Abstract: In a recent paper (Boulanger et al 2011 J. Phys. A: Math. Theor. 44 415403), cubic gravitational interactions for a massless mixed symmetry field in an AdS space have been constructed. In the current paper, we extend these results to the case of massive field. We work in a Fradkin–Vasiliev approach and use a frame-like gauge-invariant description for the massive field which works in the AdS spaces with arbitrary values of the cosmological constant including a flat Minkowski space. In this, the massless limit in the AdS space coincides with the results of Boulanger et al (2011) while we show that it is impossible to switch on a gravitational interaction for the massless field in the dS space.

39 citations