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

TL;DR

This paper develops an ambient space approach to analyze boundary values of gauge fields in AdS spacetime, providing a covariant, local formulation and extending to various gauge theories with connections to boundary dynamics.

Contribution

It introduces a manifestly covariant ambient framework for boundary analysis of AdS gauge fields, including Fronsdal, conformal currents, and shadow fields, and relates to unfolded boundary dynamics.

Findings

A local, covariant boundary formulation for massless symmetric tensor gauge fields.

Ambient description of Fronsdal, conformal currents, and shadow fields.

Extension of the approach to general gauge theories and boundary dynamics.

Abstract

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.