Model-Dependence of Minimal-Twist OPEs in $d>2$ Holographic CFTs

TL;DR

This paper investigates the dependence of minimal-twist stress tensor operators in higher-dimensional holographic CFTs, showing their three-point couplings are generally independent of gravitational action but can be affected by additional interactions and higher-spin effects.

Contribution

It provides a proof of the gravitational action independence of certain three-point couplings and analyzes how these couplings are modified by interactions in AdS and the dual CFT.

Findings

Three-point couplings are independent of pure gravitational action.

Interactions can modify minimal-twist couplings when certain three-point functions are non-zero.

Higher-spin gap scale influences the perturbative dependence of OPE coefficients.

Abstract

Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge $C_T$, we clarify the properties of stress tensor composite primary operators of minimal twist, $[T^m]$, using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling $\langle \mathcal{O}_L\mathcal{O}_L [T^m]\rangle$, where $\mathcal{O}_L$ is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling $\langle TT \mathcal{O}_L\rangle$, the three-point coupling $\langle \mathcal{O}_L\mathcal{O}_L [T^2]\rangle$ is modified at large $C_T$ if $\langle TT\mathcal{O}_L \rangle \sim \sqrt{C_T}$. This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to $\mathcal{O}_L$ can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-$\ell \geq 2$ bulk field at tree level, or any spin $\ell$ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.