Loops in AdS: from the spectral representation to position space. Part III

We study loop amplitudes in anti de-Sitter space via the spectral representation.We consider loops of spinning fields and in particular gauge fields, and derive variousidentities connecting different families of loop diagrams, at different number of loops, differentspins, different masses. Such identities are useful for the computation of Witten diagrams.Considering the theory of large-N-f conformal scalar QED defined on AdS space, we derivean analytic expression for the exact 4-point correlation function at sub-leading order in1/N-f. Additionally, we derive analytic expressions for bulk 2-point functions and boundary 4-pointfunctions for various families of diagrams, which we denote as "blob diagrams". Finally westudy 4-point ladder diagrams with spinning fields, and we derive integral expressions forthe spectral representation of ak-loop ladder diagram