Notes on the ambient approach to boundary values of AdS gauge fields

The ambient space of dimension d+2 allows to formulate both fields on AdS(d+1) and conformal fields in d dimensions such that the symmetry algebra o(d,2) is realized linearly. We elaborate an ambient approach to the boundary analysis of gauge fields on anti de Sitter spacetime. More technically, we use its parent extension where fields are still defined on AdS or conformal space through arbitrary intrinsic coordinates while the ambient construction works in the target space. In this way, a manifestly local and o(d,2)-covariant formulation of the boundary behaviour of massless symmetric tensor gauge fields on AdS(d+1) spacetime is obtained. As a byproduct, we identify some useful ambient formulation for Fronsdal fields, conformal currents and shadow fields along with a concise generating-function formulation of the Fradkin-Tseytlin conformal fields somewhat similar to the one obtained by Metsaev. We also show how this approach extends to more general gauge theories and discuss its relation to the unfolded derivation of the boundary dynamics recently proposed by Vasiliev.Comment: Slightly expanded version of the invited contribution to the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasiliev; version 2: addition of 2 references, some comparisons with the standard AdS/CFT framework and comments on the scalar singleton cas

On gravitational interactions for massive higher spins in AdS3AdS_3

In this paper we investigate gravitational interactions of massive higher spin fields in three dimensional $AdS$ space with arbitrary value of cosmological constant including flat Minkowski space. We use frame-like gauge description for such massive fields adopted to three-dimensional case. At first, we carefully analyze the procedure of switching on gravitational interactions in the linear approximation on the example of massive spin-3 field and then proceed with the generalization to the case of arbitrary integer spin field. As a result we construct a cubic interaction vertex linear in spin-2 field and quadratic in higher spin field on $AdS_3$ background. As in the massless case the vertex does not contain any higher derivative corrections to the Lagrangian and/or gauge transformations. Thus, even after switching on gravitational interactions, one can freely consider any massless or partially massless limits as well as the flat one.Comment: 21 pages. Some clarifications and 1 new reference added. Version to appear in the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasilie

Propagating modes of non-Abelian tensor gauge field of second rank

In the recently proposed extension of the YM theory, non-Abelian tensor gauge field of the second rank is represented by a general tensor whose symmetric part describes the propagation of charged gauge boson of helicity two and its antisymmetric part - the helicity zero charged gauge boson. On the non-interacting level these polarizations are similar to the polarizations of the graviton and of the Abelian antisymmetric B field, but the interaction of these gauge bosons carrying non-commutative internal charges cannot be directly identified with the interaction of gravitons or B field. Our intention here is to illustrate this result from different perspectives which would include Bianchi identity for the corresponding field strength tensor and the analysis of the second-order partial differential equation which describes in this theory the propagation of non-Abelian tensor gauge field of the second rank.Comment: 22 pages, Latex fil