The continuous spin limit of higher spin field equations

We show that the Wigner equations describing the continuous spin representations can be obtained as a limit of massive higher-spin field equations. The limit involves a suitable scaling of the wave function, the mass going to zero and the spin to infinity with their product being fixed. The result allows to transform the Wigner equations to a gauge invariant Fronsdal-like form. We also give the generalisation of the Wigner equations to higher dimensions with fields belonging to arbitrary representations of the massless little group.Comment: 18 pages, JHEP style. Typos corrected, references adde

How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples

Aiming at non-experts, we explain the key mechanisms of higher-spin extensions of ordinary gravity. We first overview various no-go theorems for low-energy scattering of massless particles in flat spacetime. In doing so we dress a dictionary between the S-matrix and the Lagrangian approaches, exhibiting their relative advantages and weaknesses, after which we high-light potential loop-holes for non-trivial massless dynamics. We then review positive yes-go results for non-abelian cubic higher-derivative vertices in constantly curved backgrounds. Finally we outline how higher-spin symmetry can be reconciled with the equivalence principle in the presence of a cosmological constant leading to the Fradkin--Vasiliev vertices and Vasiliev's higher-spin gravity with its double perturbative expansion (in terms of numbers of fields and derivatives).Comment: LaTeX, 50 pages, minor changes, many refs added; version accepted for publication in Reviews of Modern Physic

Massless spin-two field S-duality

We present a review of the homological algebra tools involved in the standard de Rham theory and their subsequent generalizations relevant for the understanding of free massless higher spin gauge structure. M-theory arguments suggest the existence of an extension of (Abelian) S-duality symmetry for non-Abelian gauge theories, like the four dimensional Yang-Mills or Einstein theories. Some no-go theorems prove that this extension, if it exists, should fall outside the scope of local perturbative field theory

Consistent couplings between spin-2 and spin-3 massless fields

We solve the problem of constructing consistent first-order cross-interactions between spin-2 and spin-3 massless fields in flat spacetime of arbitrary dimension n > 3 and in such a way that the deformed gauge algebra is non-Abelian. No assumptions are made on the number of derivatives involved in the Lagrangian, except that it should be finite. Together with locality, we also impose manifest Poincare invariance, parity invariance and analyticity of the deformations in the coupling constants.Comment: LaTeX file. 29 pages, no figures. Minor corrections. Accepted for publication in JHE

Current Exchanges for Reducible Higher Spin Multiplets and Gauge Fixing

We compute the current exchanges between triplets of higher spin fields which describe reducible representations of the Poincare group. Through this computation we can extract the propagator of the reducible higher spin fields which compose the triplet. We show how to decompose the triplet fields into irreducible HS fields which obey Fronsdal equations, and how to compute the current-current interaction for the cubic couplings which appear in ArXiv:0708.1399 [hep-th] using the decomposition into irreducible modes. We compare this result with the same computation using a gauge fixed (Feynman) version of the triplet Lagrangian which allows us to write very simple HS propagators for the triplet fields.Comment: 26 pages, 1 table; v3 some clarifications and references added, typos corrected. Published versio

Consistent deformations of [p,p]-type gauge field theories

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.Comment: 17 pages, details of a proof added, accepted for publication in JHE

Tensor gauge fields in arbitrary representations of GL(D,R): II. Quadratic actions

Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in D-dimensional Minkowski space are explicitly written in a compact form by making use of Levi-Civita tensors. The field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non-Lagrangian local field equations proposed previously. Moreover, these actions allow a frame-like reformulation a la MacDowell-Mansouri, without any trace constraint in the tangent indices.Comment: LaTeX, 53 pages, no figure. Accepted for publication in Communications in Mathematical Physics. Local Fierz-Pauli programme achieved by completing the analysis of Labastid

Higher-order singletons and partially massless fields

Based on the talk given by X.B. at the international conference “Mathematics Days in Sofia” held in July 2014 at Sofia (Bulgaria)We review the following higher-spin holographic duality conjecture: the O(N) model at an isotropic Lifshitz point of criticality order l+1 should be dual to a higher-spin gravity theory whose spectrum contains a tower of partially massless symmetric tensor fields of all even spins and all odd depths between 1 and 2l−1. More precisely, the Gaussian fixed point corresponding to free higher-order singletons on the d-dimensional boundary should be de-scribed in the bulk by the Vasiliev equations based on the symmetry algebra of the polywave equation of order 2l. Moreover, an elementary renormalization group analysis suggests that for l=2 and 5<d<11 both the free and the interacting isotropic Lifshitz point should be described by the same bulk theory but with distinct boundary conditions