Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra

The generalized connections of the (anti)-de Sitter space symmetry algebra, which are differential forms of arbitrary degree with values in any irreducible (spin)-tensor representation of the (anti)-de Sitter algebra, are studied. It is shown that arbitrary-spin gauge field in (anti)-de Sitter space, massless or partially-massless, can be described by a single connection. A 'one-to-one' correspondence between the connections of the (anti)-de Sitter algebra and the gauge fields is established. The gauge symmetry is manifest and auxiliary fields are automatically included in the formalism.Comment: 37 pages; comments on p.24-25 are extended; references adde

Mixed-Symmetry Massless Fields in Minkowski space Unfolded

The unfolded formulation for arbitrary massless mixed-symmetry bosonic and fermionic fields in Minkowski space is constructed. The unfolded form is proved to be uniquely determined by the requirement that all gauge symmetries are manifest. The unfolded equations have the form of a covariant constancy condition. The gauge fields and gauge parameters are differential forms with values in certain irreducible Lorentz tensors. The unfolded equations for bosons determine completely those for fermions. The proposed unfolded formulation also contains dual formulations for massless mixed-symmetry fields.Comment: 59 pages; PDOF counting added; typos correcte

Towards higher spin holography in ambient space of any dimension

We derive the propagators for higher-spin master fields in anti-de Sitter space of arbitrary dimension. A method is developed to construct the propagators directly without solving any differential equations. The use of the ambient space, where AdS is represented as a hyperboloid and its conformal boundary as a projective light-cone, simplifies the approach and makes a direct contact between boundary-to-bulk propagators and two-point functions of conserved currents

On Locality, Holography and Unfolding

We study the functional class and locality problems in the context of higher-spin theories and Vasiliev's equations. A locality criterion that is sufficient to make higher-spin theories well-defined as field theories on Anti-de-Sitter space is proposed. This criterion identifies admissible pseudo-local field redefinitions which preserve AdS/CFT correlation functions as we check in the 3d example. Implications of this analysis for known higher-spin theories are discussed. We also check that the cubic coupling coefficients previously fixed in 3d at the action level give the correct CFT correlation functions upon computing the corresponding Witten diagrams.Comment: 36 pages, LaTex. References added, typos corrected. Final version to appear in JHE

Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality

The formal algebraic structures that govern higher-spin theories within the unfolded approach turn out to be related to an extension of the Kontsevich Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one to construct the Hochschild cocycles of higher-spin algebras that make the interaction vertices. As an application of these results we construct a family of Vasiliev-like equations that generate the Hochschild cocycles with $sp(2n)$ symmetry from the corresponding cycles. A particular case of $sp(4)$ may be relevant for the on-shell action of the $4d$ theory. We also give the exact equations that describe propagation of higher-spin fields on a background of their own. The consistency of formal higher-spin theories turns out to have a purely geometric interpretation: there exists a certain symplectic invariant associated to cutting a polytope into simplices, namely, the Alexander-Spanier cocycle.Comment: typos fixed, many comments added, 36 pages + 20 pages of Appendices, 3 figure