New Results on Holographic Three-Point Functions

TL;DR

The paper tackles the challenge of computing holographic three-point functions for active scalar operators along RG flows. It introduces a gauge invariant framework that collapses the dynamics to a second order ODE for the active scalar and permits a Green's function treatment of cubic interactions, enabling explicit derivations of the Bose symmetric ⟨O O O⟩. The authors provide a general integral expression for the three-point function and validate it by applying it to the GPPZ flow, where the bulk-to-boundary propagators are tractable and the trilinear couplings can be extracted from on-shell amplitudes. This work establishes a practical route to higher-point correlators in holographic RG flows and sets the stage for analyzing more complex mixed correlators in diverse backgrounds.

Abstract

We exploit a gauge invariant approach for the analysis of the equations governing the dynamics of active scalar fluctuations coupled to the fluctuations of the metric along holographic RG flows. In the present approach, a second order ODE for the active scalar emerges rather simply and makes it possible to use the Green's function method to deal with (quadratic) interaction terms. We thus fill a gap for active scalar operators, whose three-point functions have been inaccessible so far, and derive a general, explicitly Bose symmetric formula thereof. As an application we compute the relevant three-point function along the GPPZ flow and extract the irreducible trilinear couplings of the corresponding superglueballs by amputating the external legs on-shell.