We discuss the emergence of W-algebras as asymptotic symmetries of higher-spin gauge theories coupled to three-dimensional Einstein gravity with a negative cosmological constant. We focus on models involving a finite number of bosonic higher-spin fields, and especially on the example provided by the coupling of a spin-3 field to gravity. It is described by a SL(3) \times SL(3) Chern-Simons theory and its asymptotic symmetry algebra is given by two copies of the classical W_3-algebra with central charge the one computed by Brown and Henneaux in pure gravity with negative cosmological constant

We discuss how to systematically compute the asymptotic symmetry algebras of generic three-dimensional bosonic higher-spin gauge theories in backgrounds that are asymptotically AdS. We apply these techniques to a one-parameter family of higher-spin gauge theories that can be considered as large N limits of SL(N) × SL(N) Chern-Simons theories, and we provide a closed formula for the structure constants of the resulting infinitedimensional non-linear W-algebras. Along the way we provide a closed formula for the structure constants of all classical W N algebras. In both examples the higher-spin generators of the W-algebras are Virasoro primaries. We eventually discuss how to relate our basis to a non-primary quadratic basis that was previously discussed in literature.

This is the first of two papers devoted to the local "metric-like" unconstrained Lagrangians and field equations for higher-spin gauge fields of mixed symmetry in flat space. Here we complete the previous constrained formulation of Labastida for Bose fields. We thus recover his Lagrangians via the Bianchi identities, before extending them to their "minimal" unconstrained form with higher derivatives of the compensator fields and to yet another, non-minimal, form with only two-derivative terms. We also identify classes of these systems that are invariant under Weyl-like symmetries.

We consider the coupling of a symmetric spin-3 gauge field ϕ µνρ to three-dimensional gravity in a second order metric-like formulation. The action that corresponds to an SL(3, R) × SL(3, R) Chern-Simons theory in the frame-like formulation is identified to quadratic order in the spin-3 field. We apply our result to compute corrections to the area law for higher-spin black holes using Wald's entropy formula.

We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.

We describe the dynamics of two-dimensional relativistic and Carrollian fluids. These are mapped holographically to three-dimensional locally anti-de Sitter and locally Minkowski spacetimes, respectively. To this end, we use Eddington-Finkelstein coordinates, and grant general curved two-dimensional geometries as hosts for hydrodynamics. This requires to handle the conformal anomaly, and the expressions obtained for the reconstructed bulk metrics incorporate non-conformal-fluid data. We also analyze the freedom of choosing arbitrarily the hydrodynamic frame for the description of relativistic fluids, and propose an invariant entropy current compatible with classical and extended irreversible thermodynamics. This local freedom breaks down in the dual gravitational picture, and fluid/gravity correspondence turns out to be sensitive to dissipation processes: the fluid heat current is a necessary ingredient for reconstructing all Bañados asymptotically anti-de Sitter solutions. The same feature emerges for Carrollian fluids, which enjoy a residual frame invariance, and their Barnich-Troessaert locally Minkowski duals. These statements are proven by computing the algebra of surface conserved charges in the fluid-reconstructed bulk threedimensional spacetimes.

110 pages, LaTeX. Thanks to the referee for urging us to extend Section 4 and to add Section 3.4.1. Final version to appear in Nucl. Phys. BInternational audienceThis paper is a sequel of [A. Campoleoni, D. Francia, J. Mourad, A. Sagnotti, Nucl. Phys. B 815 (2009) 289, arXiv:0810.4350 [hep-th]], and is also devoted to the local "metric-like" unconstrained Lagrangians and field equations for higher-spin fields of mixed symmetry in flat space. Here we complete the previous constrained on-shell formulation of Labastida for Fermi fields, deriving the corresponding constrained Lagrangians both via the Bianchi identities and via the requirement of self-adjointness. We also describe two types of unconstrained Lagrangian formulations: a "minimal" one, containing higher derivatives of the compensator fields, and another non-minimal one, containing only one-derivative terms. We identify classes of these systems that are invariant under Weyl-like symmetry transformations

The asymptotic structure of three-dimensional higher-spin anti-de Sitter gravity is analyzed in the metric approach, in which the fields are described by completely symmetric tensors and the dynamics is determined by the standard Einstein-Fronsdal action improved by higher order terms that secure gauge invariance. Precise boundary conditions are given on the fields. The asymptotic symmetries are computed and shown to form a non-linear W -algebra, in complete agreement with what was found in the Chern-Simons formulation. The W -symmetry generators are two-dimensional traceless and divergenceless rank-s symmetric tensor densities of weight s (s = 2, 3, · · · ), while asymptotic symmetries emerge at infinity through the conformal Killing vector and conformal Killing tensor equations on the two-dimensional boundary, the solution space of which is infinite-dimensional. For definiteness, only the spin 3 and spin 4 cases are considered, but these illustrate the features of the general case: emergence of the W -extended conformal structure, importance of the improvement terms in the action that maintain gauge invariance, necessity of the higher spin gauge transformations of the metric, role of field redefinitions.