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 article, a two-dimensional BF theory with infinitely many higher spin fields is proposed, interpreted as the AdS 2 higher spin gravity model describing a consistent interaction between local fields in AdS 1 + 2 space including gravitational field, higher spin partially-massless fields, and dilaton fields.
Abstract: Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS
2 higher spin gravity model describing a consistent interaction between local fields in AdS
2 space including gravitational field, higher spin partially-massless fields, and dilaton fields. We carry out analysis of the frame-like and the metric-like formulation of the theory. Infinite-dimensional higher spin global algebras and their finite-dimensional truncations are realized in terms of o(2, 1) − sp(2) Howe dual auxiliary variables.
28 citations
TL;DR: In this paper, the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed two-form of ghost degree n-1, and the scalar potential ofghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory.
Abstract: We study supergeometric structures underlying frame-like Lagrangians. We show that for the theory in n space–time dimensions both the frame-like Lagrangian and its gauge symmetries are encoded in the target supermanifold equipped with the odd vector field, the closed two-form of ghost degree n-1, and the scalar potential of ghost degree n. These structures satisfy a set of compatibility conditions ensuring the gauge invariance of the theory. The Lagrangian and the gauge symmetries have the same structures as those of AKSZ sigma model so that frame-like formulation can be seen as its presymplectic generalization. In contrast to the conventional AKSZ model, the generalization allows to describe systems with local degrees of freedom in terms of finite-dimensional target space. We argue that the proposed frame-like approach is directly related de Donder–Weyl polymomentum Hamiltonian formalism. Along with the standard field-theoretical examples like Einstein–Yang–Mills theory, we consider free higher spin fields, multi-frame gravity and parametrized systems. In particular, we propose the frame-like action for free totally symmetric massless fields that involves all higher spin connections on an equal footing.
27 citations
TL;DR: In this article, non-linear equations for the formal Type-B Higher Spin Gravity model were derived from the first principles: the gauge invariance of the CFT partition function on an arbitrary background for single-trace operators.
Abstract: We propose non-linear equations for the formal Type-B Higher Spin Gravity that is dual to the free fermion or to the Gross-Neveu model, depending on the boundary conditions. The equations are directly obtained from the first principles: the gauge invariance of the CFT partition function on an arbitrary background for single-trace operators. We also get equations describing propagation of certain mixed-symmetry fields over higher spin flat backgrounds.
27 citations
TL;DR: In this paper, the Feynman rules for the minimal type higher-spin theory on AdS$d+1$ at cubic order were determined and the quantum action at cubic-order in de Donder gauge was established, including ghosts.
Abstract: We determine the Feynman rules for the minimal type A higher-spin gauge theory on AdS$_{d+1}$ at cubic order. In particular, we establish the quantum action at cubic order in de Donder gauge, including ghosts. We also give the full de Donder gauge propagators of higher-spin gauge fields and their ghosts. This provides all ingredients needed to quantise the theory at cubic order.
26 citations
TL;DR: In this paper, a generalization of the flat-space spinor-helicity formalism in four dimensions to anti-de Sitter space was proposed, and the potentials associated with the previously found plane wave solutions for field strengths were derived for lower-spin fields.
Abstract: In a recent letter we suggested a natural generalization of the flat-space spinor-helicity formalism in four dimensions to anti-de Sitter space. In the present paper we give some technical details that were left implicit previously. For lower-spin fields we also derive potentials associated with the previously found plane wave solutions for field strengths. We then employ these potentials to evaluate some three-point amplitudes. This analysis illustrates a typical computation of an amplitude without internal lines in our formalism.
23 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