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Model-dependence of minimal-twist OPEs in \(d > 2\) holographic CFTs. (English) Zbl 1456.83075
Summary: 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 \(\left\langle{\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^m\right]\right\rangle \), 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 \(\left\langle TT{\mathcal{O}}_L\right\rangle \), the three-point coupling \(\left\langle{\mathcal{O}}_L{\mathcal{O}}_L\left[{T}^2\right]\right\rangle\) is modified at large \(C_T\) if \(\left\langle TT{\mathcal{O}}_L\right\rangle \sim \sqrt{C_T} \). 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-\( \mathcal{l} \geq 2\) bulk field at tree level, or any spin \(\mathcal{l}\) at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.

MSC:
83E05 Geometrodynamics and the holographic principle
83E15 Kaluza-Klein and other higher-dimensional theories
83E50 Supergravity
83C45 Quantization of the gravitational field
81T60 Supersymmetric field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R15 Operator algebra methods applied to problems in quantum theory
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