Holographic three-point functions: one step beyond the tradition

TL;DR

This paper advances the holographic computation of three-point correlation functions along RG flows, providing explicit formulas and methods for different flows and operator insertions, including stress tensors and currents.

Contribution

It introduces a systematic procedure for calculating three-point functions in holographic RG flows, extending beyond traditional methods and addressing complex operator insertions.

Findings

Derived finite expressions for three-point functions in specific RG flows.

Computed three-point functions involving inert and active scalars, including superglueball couplings.

Outlined methods for stress tensor and R-symmetry current insertions.

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.