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

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