Construction of Bulk Fields with Gauge Redundancy

We extend the construction of field operators in AdS as smeared single trace operators in the boundary CFT to gauge fields and gravity. Bulk field operators in a fixed gauge can be thought of as non-local gauge invariant observables. Non-local commutators result from the Gauss law constraint, which for gravity implies a perturbative notion of holography. We work out these commutators in a generalized Coulomb gauge and obtain leading order smearing functions in radial gauge.