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

An action principle for Vasiliev's four-dimensional higher-spin gravity

We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge fields in four spacetime dimensions with an action principle. We first extend Vasiliev's original system with differential forms in degrees higher than one. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: One set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and another set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of ranks two or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal Type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on shell, to Vasiliev's original system.Comment: 37 pages. References added, corrected typo

Supersymmetric Higher Spin Theories

We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the $dS_4$, Euclidean and Kleinian version of these algebras, as well as the corresponding fully nonlinear Vasiliev type higher spin theories, in which the reality conditions we impose on the master fields play a crucial role. The ${\cal N}=2$ supersymmetric higher spin theory in $dS_4$, on which we elaborate further, is included in this class of models. A subset of Konstein-Vasiliev algebras are the higher spin extensions of the $AdS_4$ superalgebras $osp(4|{\cal N})$ for ${\cal N}=1,2,4$ mod 4 and can be realized using fermionic oscillators. We tensor the higher superalgebras of the latter kind with appropriate internal symmetry groups and show that the ${\cal N}=3$ mod 4 higher spin algebras are isomorphic to those with ${\cal N}=4$ mod 4. We describe the fully nonlinear higher spin theories based on these algebras as well, and we elaborate further on the ${\cal N}=6$ supersymmetric theory, providing two equivalent descriptions one of which exhibits manifestly its relation to the ${\cal N}=8$ supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Prevalence and severity of cardiac abnormalities and arteriosclerosis in farmed rainbow trout (Oncorhynchus mykiss)

Cardiovascular disease may pose a major threat to the health and welfare of farmed fish. By investigating a range of established cardiovascular disease indicators, we aimed to determine the prevalence, severity and consequences of this affliction in farmed rainbow trout (Oncorhynchus mykiss) from an open cage farm in the Baltic Sea, an open cage farm in a freshwater lake, and a land-based recirculating aquaculture system. We also aimed to identify environmental, anthropogenic and physiological factors contributing towards the development of the disease. The majority of trout possessed enlarged hearts with rounded ventricles (mean height:width ratios of 1.0-1.1 c.f. similar to 1.3 in wild fish) and a high degree of vessel misalignment (mean angles between the longitudinal ventricular axis and the axis of the bulbus arteriosus of 28-31 degrees c.f. similar to 23 degrees in wild fish). The prevalence and severity of coronary arteriosclerosis was also high, as 92-100% of fish from the different aquaculture facilities exhibited coronary lesions. Mean lesion incidence and severity indices were 67-95% and 3.1-3.9, respectively, which resulted in mean coronary arterial blockages of 19-32%. To evaluate the functional significance of these findings, we modelled the effects of arterial blockages on coronary blood flow and experimentally tested the effects of coronary occlusion in a sub-sample of fish. The observed coronary blockages were estimated to reduce coronary blood flow by 34-54% while experimental coronary occlusion adversely affected the electrocardiogram of trout. Across a range of environmental (water current, predation), anthropogenic (boat traffic intensity, hatchery of origin, brand of feed pellets) and physiological factors (condition factor, haematological and plasma indices), the hatchery of origin was the main factor contributing towards the observed variation in the development of cardiovascular disease. Therefore, further research on the effects of selective breeding programs and rearing strategies on the development of cardiovascular disease is needed to improve the welfare and health of farmed fish

Analysis of Higher Spin Field Equations in Four Dimensions

The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s=0,2,4,.. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the higher spin gauge fields as weak perturbations. We also give the details of an explicit iteration procedure for obtaining the field equations to arbitrary order in curvatures. In particular, we highlight the structure of all the quadratic terms in the field equations.Comment: Latex, 30 pages, several clarifications and few references adde

Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism

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.Comment: Corrected typos, references added, two figures, some remarks and two subsections added for clarit

Deformation independent open brane metrics and generalized theta parameters

We investigate the consequences of generalizing certain well established properties of the open string metric to the conjectured open membrane and open Dp-brane metrics. By imposing deformation independence on these metrics their functional dependence on the background fields can be determined including the notorious conformal factor. In analogy with the non-commutativity parameter $\Theta^{\mu\nu}$ in the string case, we also obtain `generalized' theta parameters which are rank q+1 antisymmetric tensors (polyvectors) for open Dq-branes and rank 3 for the open membrane case. The expressions we obtain for the open membrane quantities are expected to be valid for general background field configurations, while the open D-brane quantities are only valid for one parameter deformations. By reducing the open membrane data to five dimensions, we show that they, modulo a subtlety with implications for the relation between OM-theory and NCYM, correctly generate the open string and open D2-data.Comment: 24 pages, LaTe

A minimal BV action for Vasiliev's four-dimensional higher spin gravity

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle.Comment: 39 pages, 1 figure. Additional comments in the conclusion

Black holes in three dimensional higher spin gravity: A review

We review recent progress in the construction of black holes in three dimensional higher spin gravity theories. Starting from spin-3 gravity and working our way toward the theory of an infinite tower of higher spins coupled to matter, we show how to harness higher spin gauge invariance to consistently generalize familiar notions of black holes. We review the construction of black holes with conserved higher spin charges and the computation of their partition functions to leading asymptotic order. In view of the AdS/CFT correspondence as applied to certain vector-like conformal field theories with extended conformal symmetry, we successfully compare to CFT calculations in a generalized Cardy regime. A brief recollection of pertinent aspects of ordinary gravity is also given.Comment: 49 pages, harvmac, invited contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry

We provide Vasiliev's four-dimensional bosonic higher-spin gravities with six families of exact solutions admitting two commuting Killing vectors. Each family contains a subset of generalized Petrov Type-D solutions in which one of the two so(2) symmetries enhances to either so(3) or so(2,1). In particular, the spherically symmetric solutions are static and we expect one of them to be gauge-equivalent to the extremal Didenko-Vasiliev solution given in arXiv:0906.3898. The solutions activate all spins and can be characterized either via generalized electric and magnetic charges defined asymptotically in weak-field regions or via the values of fully higher-spin gauge-invariant observables given by on-shell closed zero-forms. The solutions are obtained by combining the gauge-function method with separation of variables in twistor space via expansion of the Weyl zero-form in Di-Rac supersingleton projectors times deformation parameters in a fashion that is suggestive of a generalized electromagnetic duality.Comment: v1: 77 pages; 3 tables; 23 pages of appendices. v2: 5 additional pages of clarifications, typos correcte