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

The ambient space allows us to formulate both fields on AdS d + 1 and conformal fields in d dimensions such that the symmetry algebra is realized linearly. We elaborate an ambient approach to the boundary analysis of gauge fields on AdS d + 1 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 -covariant formulation of the boundary behavior 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. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.