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 authors show that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions.
Abstract: Generating functions encoding cubic interactions of (partially-)massless higher- spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factor- ized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.
109 citations
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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.
84 citations
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TL;DR: In this paper, a pedagogical account of higher-spin fields and their connections with string theory is given, and the key no-go and yes-go results concerning higher spin interactions are reviewed.
Abstract: A contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the motivations for and a brief historical overview of the subject. We discuss the Wigner classifications of unitary irreducible Poincar\'e-modules, write down covariant field equations for totally symmetric massive and massless representations in flat space, and consider their Lagrangian formulation. After an elementary exposition of the AdS unitary representations, we review the key no-go and yes-go results concerning higher-spin interactions, e.g., the Velo-Zwanziger acausality and its string-theoretic resolution among others. The unfolded formalism, which underlies Vasiliev's equations, is then introduced to reformulate the flat-space Bargmann-Wigner equations and the AdS massive-scalar Klein-Gordon equation, and to state the "central on-mass-shell theorem". These techniques are used for deriving the unfolded form of the boundary-to-bulk propagator in $AdS_4$, which in turn discloses the asymptotic symmetries of (supersymmetric) higher-spin theories. The implications for string-higher-spin dualities revealed by this analysis are then elaborated.
77 citations
TL;DR: In this article, the deformations of higher-spin symmetries induced by cubic interactions of symmetric massless bosonic fields are analyzed within the metric-like formalism.
Abstract: The deformations of higher-spin symmetries induced by cubic interactions of symmetric massless bosonic fields are analyzed within the metric-like formalism. Our analysis amends the existing classification according to gauge-algebra deformations taking into account also gauge-transformation deformations. In particular, we identify a class of couplings which leave the gauge algebra Abelian but deform one (out of three) gauge transformation, and another class of couplings which deform all three gauge transformations in (A)dS but only two in the flat-space limit. The former class is related to higher-spin algebra multiplets (representations of the global algebra) together with the massless-massive-massive couplings which we also briefly discuss. The latter class is what makes (A)dS a distinguished background for higher-spin interactions and includes in particular the gravitational interactions of higher-spin fields, retrospectively accounting for the Fradkin-Vasiliev solution to the Aragone-Deser problem. We also study the restriction of gauge symmetries to global symmetries (higher-spin algebra) discussing the invariant bilinear form and the cyclicity of the structure constants. A possible generalization of the analysis to partially-massless fields is also commented.
74 citations
TL;DR: In this article, the anomalous dimensions and OPE coefficients of infinite classes of scalar local operators were computed using CFT data. But they were not applied to non-unitary theories.
Abstract: We describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ϵ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N)-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.
67 citations
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TL;DR: In this article, nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented, and a nonlinear nonlinear model of the field equations is proposed.
756 citations
TL;DR: In this paper, consistent equations of motion of interacting gauge fields of all spins in 3+1 dimensions are formulated in a closed form, which are explicitly general coordinate invariant, possess all necessary higher spin gauge symmetries and reduce to the usual equations of free massless fields at the linearized level.
754 citations
TL;DR: In this article, a unified geometric formulation of gravitation and supergravity is presented, which is constructed out of the components of the curvature tensor for bundle spaces with four-dimensional Lorentz base manifold and structure groups Sp(4) for gravity and OSp(1, 4) for supergravity.
Abstract: A unified geometric formulation of gravitation and supergravity is presented. The action for these theories is constructed out of the components of the curvature tensor for bundle spaces with four-dimensional Lorentz base manifold and structure groups Sp(4) for gravity and OSp(1,4) for supergravity. The requirement of invariance under reflections, local Lorentz transformations, and general coordinate transformations uniquely determines the action and ensures the existence of local supersymmetry in supergravity.
744 citations
TL;DR: In this article, the cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin are computed in a self-contained manner, with the sources of the BRST variations of the fields included in the problem.
611 citations
TL;DR: In this paper, nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented, and a nonlinear nonlinear model of the field equations is proposed.
Abstract: Nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented.
587 citations