Holographic three-point functions: one step beyond the tradition

TL;DR

The paper addresses the problem of computing three-point functions along holographic RG flows, going beyond standard two-point checks. It combines holographic renormalization with tree-level bulk cubic couplings to derive finite, explicit expressions for three-point functions in two representative flows: the CB flow (inert scalars) and the GPPZ flow (two inert, one active scalar with stress-tensor mixing). The CB results yield a compact, finite expression for the inert-scalar three-point function and clarify its UV behavior, while the GPPZ analysis handles mixing with the metric, identifies necessary logarithmic counterterms, and extracts a finite on-shell trilinear vertex with a clear superglueball interpretation. The work demonstrates a practical route to higher-point holographic correlators, sets the stage for including stress-tensor and current insertions, and offers precise strong-coupling predictions for three-body interactions in these holographic models.

Abstract

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 CPO's dual to inert scalars. In the GPPZ flow, that captures some features of N=1 SYM theory, we 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 trilinear coupling 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.