Want to know how to explicitly map the fields in the AdS symmetric theory to those in the conformally symmetric theory and extend this calculation to other symmetries? Then check out the latest work by my hometown hero, Dr. Jeffrey Hazboun.
Hazboun (2018). Constructing an explicit AdS/CFT correspondence with Cartan geometry. Nuclear Physics B. Volume 929, Pages 254-265. DOI: 10.1016/j.nuclphysb.2018.02.006