Non-abelian cubic vertices for higher-spin fields in AdS(d)
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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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
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
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
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
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
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TL;DR: The manifestly gauge invariant formulation for free symmetric higher-spin partially massless fields in ( A dS d) is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of ( o ( d − 1, 2 ) ) o( d, 1 ) described by two-row Young tableaux, in which the lengths of the first and second row are associated with the spin and depth of partial masslessness as mentioned in this paper.
156 citations
TL;DR: In this paper, a review is devoted to the intriguing and still largely unexplored links between string theory and higher spins, the types of excitations that lie behind their most cherished properties.
Abstract: This review is devoted to the intriguing and still largely unexplored links between string theory and higher spins, the types of excitations that lie behind their most cherished properties. A closer look at higher spin fields provides some further clues that string theory describes a broken phase of a higher spin gauge theory. Conversely, string amplitudes contain a wealth of information on higher spin interactions that can clarify long-standing issues related to their infrared behavior.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.
145 citations
TL;DR: An off-shell generating function for all cubic interactions of higher spin gauge fields constructed in Manvelyan et al. as discussed by the authors is a generalization of the Sagnotti and Taronna [2], and turns out to have a remarkable structure.
144 citations
TL;DR: In this paper, the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds has been analyzed for Weyl zero-form modules and their duals, and the unfolded notion of local degrees of freedom has been discussed.
Abstract: We present some generalities of unfolded on-shell dynamics that are useful in analysing the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra modules generated from primary Weyl tensors of arbitrary mass and shape, and in backgrounds with general values of the cosmological constant. We also discuss the unfolded notion of local degrees of freedom in theories with and without gravity and with and without massive deformation parameters, using the language of Weyl zero-form modules and their duals.
140 citations
TL;DR: In this article, a frame-like covariant Lagrangian formulation of higher spin massless fields propagating on the AdS d background is proposed, where higher spin fields are described in terms of gauge p -forms which carry tangent indices representing certain traceless tensor or gamma transversal spinor-tensor representations.
129 citations