New Results on Holographic Three-Point Functions

TL;DR

This paper introduces a gauge invariant method to compute three-point functions of active scalar operators in holographic RG flows, enabling new calculations of superglueball interactions.

Contribution

It develops a simplified second order ODE approach and Green's function method for active scalar three-point functions in holography, filling a previous gap in the field.

Findings

Derived explicit Bose symmetric three-point function formula.

Computed three-point functions along the GPPZ flow.

Extracted superglueball couplings from the three-point functions.

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.