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

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 $⟨{\mathcal{O}}_L{\mathcal{O}}_L[T^m]⟩$, 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 $⟨TT{\mathcal{O}}_L⟩$, the three-point coupling $⟨{\mathcal{O}}_L{\mathcal{O}}_L[T^2]⟩$ is modified at large $C_T$ if $⟨TT{\mathcal{O}}_L⟩\sim \sqrt{C_T}$. 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-$\ell \ge 2$ 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.

arXiv comment25+10 pages

References in corpus (21)

• Gauge Theory Correlators from Non-Critical String Theory
• A bound on chaos
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Analyticity in Spin in Conformal Theories
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Unitarity and the Holographic S-Matrix
• Effective Conformal Theory and the Flat-Space Limit of AdS
• Loops in AdS from Conformal Field Theory
• A Proof of the Conformal Collider Bounds
• Weight Shifting Operators and Conformal Blocks
• Conformal correlators of mixed-symmetry tensors
• Spinning Witten Diagrams
• Conformal Collider Physics from the Lightcone Bootstrap
• Eikonalization of Conformal Blocks
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Unitarity Methods in AdS/CFT
• Universal Lowest-Twist in CFTs from Holography
• Holographic OPE Coefficients from AdS Black Holes with Matters
• Leading Multi-Stress Tensors and Conformal Bootstrap
• Heavy-light Bootstrap from Lorentzian Inversion Formula
• Multi-stress tensors and next-to-leading singularities in the Regge limit

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• Thermal Stress Tensor Correlators, OPE and Holography
• On Local and Integrated Stress-Tensor Commutators
• $d>2$ Stress-Tensor OPE near a Line
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• Freedom near Lightcone and ANEC Saturation
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• On the Stress Tensor Light-ray Operator Algebra