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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 paper, it was shown that there is a unique Poincare invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant.
Abstract: Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the Yang-Mills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincare invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the Yang-Mills coupling is therefore rederived through cohomological arguments.

60 citations

Journal ArticleDOI
TL;DR: Using the light-cone formalism and the language of highest weight representations, this article constructed a full list of cubic interaction vertices for totally symmetric and mixed symmetry massless representations of the Poincare group in D = 6 space-time.

59 citations

Journal ArticleDOI
TL;DR: In this article, the authors analyze partially massless (PM) spin 2 and find that both its gravitational coupling and nonlinear extensions suffer from the usual background-and self-coupling difficulties: Consistent free field propagation does not extend beyond background Einstein geometries.
Abstract: We show that higher spin systems specific to cosmological spaces are subject to the same problems as models with Poincare limits. In particular, we analyze partially massless (PM) spin 2 and find that both its gravitational coupling and nonlinear extensions suffer from the usual background- and self-coupling difficulties: Consistent free field propagation does not extend beyond background Einstein geometries. Then (using conformal, Weyl, gravity, which contains relative ghost PM and graviton excitations) we find that avoiding graviton ghosts restricts Weyl-generated PM self-couplings to the usual, leading, safe, Noether current cubic ones.

58 citations

Journal ArticleDOI
TL;DR: In this paper, the Fradkin-Vasiliev type theory of higher spin fields in AdS(5) was formulated and the corresponding action functional describes cubic order approximation to gravitational interactions of bosonic mixed-symmetry fields of a particular "hook" symmetry type and totally symmetric bosonic and fermionic fields.
Abstract: We formulate Fradkin-Vasiliev type theory of massless higher spin fields in AdS(5). The corresponding action functional describes cubic order approximation to gravitational interactions of bosonic mixed-symmetry fields of a particular "hook" symmetry type and totally symmetric bosonic and fermionic fields.

57 citations

Journal ArticleDOI
TL;DR: In this article, a frame-like gauge invariant description for massive mixed symmetry tensor fields corresponding to arbitrary Young tableau with two rows was given. But the construction of this description is not complete.

55 citations