On simple models of AdS/CFT

The canonical examples AdS/CFT pairs enjoy "the conservation of difficulty" principle: perturbative regimes on both sides of the duality do not overlap, which so far prevented us from having an example with a complete proof/understanding of the duality. I will discuss two simple cases where a complete proof of AdS/CFT duality can be achieved, not without a price to pay: phi-fourth theory and chiral higher spin gravity. Based on the first model I will also discuss loop corrections in (A)dS, while the usefulness of the second model is related to 3d bosonization duality.