On three-point correlation functions in the gauge/gravity duality

TL;DR

This paper investigates how deformations affect operator renormalization in conformal field theories, using integrability and gauge/gravity duality to compute couplings and anomalous dimensions, with applications to N=4 SYM.

Contribution

It introduces a scheme to compute operator couplings under deformations and applies integrability and holography to evaluate these in N=4 SYM.

Findings

Computed one-loop couplings between the Lagrangian and large operators.

Derived deformed anomalous dimension matrices using integrability.

Validated strong coupling predictions with gauge/gravity duality.

Abstract

We study the effect of marginal and irrelevant deformations on the renormalization of operators near a CFT fixed point. New divergences in a given operator are determined by its OPE with the operator D that generates the deformation. This provides a scheme to compute the couplings a_DAB between the operator D and two arbitrary operators O_A and O_B. We exemplify for the case of N=4 SYM, considering the simplest case of the exact Lagrangian deformation. In this case the deformed anomalous dimension matrix is determined by the derivative of the anomalous dimension matrix with respect to the coupling. We use integrability techniques to compute the one-loop couplings a_LAB between the Lagrangian and two distinct large operators built with Magnons, in the SU(2) sector of the theory. Then we consider a_DAA at strong coupling, and show how to compute it using the gauge/gravity duality, when D is a chiral operator dual to any supergravity field and O_A is dual to a heavy string state. We exemplify for the Lagrangian and operators O_A dual to heavy string states, showing agreement with the prediction derived from the renormalization group arguments.