Loop Diagrams in Anti-deSitter Space

We compute a family of scalar loop diagrams in AdS. We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree-level diagrams. An important example is the computation of the finite coupling 4-point function of the large-N critical O(N) model on AdS3. Remarkably, the re-summation of bubble diagrams is equal to a certain contact diagram. Another example is a scalar with φ 4 or φ 3 coupling in AdS3, in which we compute various 4-point loop bubble diagrams. We comment on our previous work, in which we showed that the spectral representation can be used to solve the large-N O(N) and Gross Neveu models on AdS.