All correlation functions of conserved currents of the CFT that is dual to unbroken Vasiliev theory are found as invariants of higher-spin symmetry in the bulk of AdS. The conformal and higher-spin symmetry of the correlators as well as the conservation of currents are manifest, which also provides a direct link between the Maldacena-Zhiboedov result and higher-spin symmetries. Our method is in the spirit of AdS/CFT, though we never take any boundary limit or compute any bulk integrals. Boundary-to-bulk propagators are shown to exhibit an algebraic structure, living at the boundary of SpH(4), semidirect product of Sp(4) and the Heisenberg group. N-point correlation function is given by a product of N elements. * didenko@lpi.ru † skvortsov@lpi.ru 1

The manifestly gauge invariant formulation for free symmetric higher-spin partially massless fields in (A)dS d is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of (o(d−1, 2)) o(d, 1) described by two-row Young tableaux, in which the lengths of the first and second row are, respectively, associated with the spin and depth of partial masslessness.

We consider four-dimensional higher-spin (HS) theory at the first nontrivial order corresponding to the cubic action. All HS interaction vertices are explicitly obtained from Vasiliev's equations. In particular, we obtain the vertices that are not determined solely by the HS algebra structure constants. The dictionary between the Fronsdal fields and HS connections is found and the corrections to the Fronsdal equations are derived. These corrections turn out to involve derivatives of arbitrary order. We observe that the vertices not determined by the HS algebra produce naked infinities, when decomposed into the minimal derivative vertices and improvements. Therefore, standard methods can only be used to check a rather limited number of correlation functions within the HS AdS/CFT duality. A possible resolution of the puzzle is discussed.

We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields -the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local.