Carlo Iazeolla

Biaxially symmetric solutions to 4D higher spin gravity

We review some aspects of biaxially symmetric solutions to Vasiliev?s equations in four-dimensional spacetime with a negative cosmological constant. The solutions, which activate bosonic fields of all spins, are constructed using gauge functions, projectors and deformed oscillators. The deformation parameters, which are formally gauge invariant, are related to generalized electric and magnetic charges in asymptotic weak-field regions. Alternatively, the solutions can be characterized in a dual fashion using 0-form charges which are higher spin Casimir invariants built from combinations of curvatures and all their derivatives that are constant on shell and well-defined everywhere.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Higher spin theories and holography?.

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.

Unfolding mixed-symmetry fields in AdS and the BMV conjecture: II. Oscillator realization

Following the general formalism presented in arXiv:0812.3615 — referred to as Paper I — we derive the unfolded equations of motion for tensor fields of arbitrary shape and mass in constantly curved backgrounds by radial reduction of Skvortsovs equations in one higher dimension. The complete unfolded system is embedded into a single master field, valued in a tensorial Schur module realized equivalently via either bosonic (symmetric basis) or fermionic (anti-symmetric basis) vector oscillators. At critical masses the reduced Weyl zero-form modules become indecomposable. We explicitly project the latter onto the submodules carrying Metsaevs massless representations. The remainder of the reduced system contains a set of Stuckelberg fields and dynamical potentials that leads to a smooth flat limit in accordance with the Brink-Metsaev-Vasiliev (BMV) conjecture. In the unitary massless cases in AdS, we identify the Alkalaev-Shaynkman-Vasiliev frame-like potentials and explicitly disentangle their unfolded field equations.

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

A bstractWe 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

A fiber approach to harmonic analysis of unfolded higher-spin field equations

\mathfrak{s}\mathfrak{o}

Real forms of complex higher spin field equations and new exact solutions

(2) symmetries enhances to either

Quantum theories of (p; q)-forms

\mathfrak{s}\mathfrak{o}

On big crunch solutions in Prokushkin-Vasiliev theory

(3) or

4D higher spin black holes with nonlinear scalar fluctuations

\mathfrak{s}\mathfrak{o}

FRW and domain walls in higher spin gravity

(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 [1]. 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.