Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs
Fitzpatrick, A. Liam; Huang, Kuo-Wei; Meltzer, David; Perlmutter, Eric; Simmons-Duffin, David
Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge CT, we clarify the properties of stress tensor composite primary operators of minimal twist, [Tm], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling ⟨𝒪𝐿𝒪𝐿[𝑇𝑚]⟩, where 𝒪𝐿 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 ⟨𝑇𝑇𝒪𝐿⟩, the three-point coupling ⟨𝒪𝐿𝒪𝐿[𝑇2]⟩ is modified at large CT if ⟨𝑇𝑇𝒪𝐿⟩∼𝐶𝑇‾‾‾√. 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 𝒪𝐿 can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.
↧
