"Loops in AdS and Renormalisation"

I will start by setting up a renormalised AdS/CFT dictionary, accounting for both UV and IR divergences in AdS. IR divergences are dealt with by boundary counterterms, as in holographic renormalization at tree-level, and UV divergences by renormalizing the bulk action. I will show that AdS amplitudes, to all orders in perturbation theory, are CFT correlators by showing that they satisfy the CFT Ward identities. I will then discuss new methodology for computing loop diagrams in AdS that makes full use of AdS isometries, and illustrate the discussion with a 2-loop computation in Phi^4 theory in AdS.