Holographic three-point functions: one step beyond the tradition

Within the program of holographic renormalization, we discuss the computation of three-point correlation functions along RG flows. We illustrate the procedure in two simple cases. In an RG flow to the Coulomb branch of N=4 SYM theory we derive a compact and finite expression for the three-point function of lowest CPOs dual to inert scalars. In the GPPZ flow, that captures some features of N=1 SYM theory, we identify two new logarithmically divergent counterterms and compute the three-point function with insertion of two inert scalars and one active scalar that mixes with the stress tensor. By amputating the external legs at the mass poles we extract the finite and scheme independent trilinear couplings of the corresponding superglueballs. Finally we outline the procedure for computing three-point functions with insertions of the stress tensor as well as of (broken) R-symmetry currents