Einstein gravity from ANEC correlators

Abstract

We study correlation functions with multiple averaged null energy (ANEC) operators in conformal field theories. For large $N$ CFTs with a large gap to higher spin operators, we show that the OPE between a local operator and the ANEC can be recast as a particularly simple differential operator acting on the local operator. This operator is simple enough that we can resum it and obtain the finite distance OPE. Under the large $N$ - large gap assumptions, the vanishing of the commutator of ANEC operators tightly constrains the OPE coefficients of the theory. An important example of this phenomenon is the conclusion that $a=c$ in $d=4$. This implies that the bulk dual of such a CFT is semi-classical Einstein-gravity with minimally coupled matter.

32 pages + appendices, 6 figures; v2:typos corrected and a comment added in introduction

References in corpus (17)

• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• Viscosity Bound and Causality Violation
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Light-ray operators in conformal field theory
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Bounds for OPE coefficients on the Regge trajectory
• Goldstone modes and photonization for higher form symmetries
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• Fast Conformal Bootstrap and Constraints on 3d Gravity
• Light-ray Operators and the BMS Algebra
• The Holographic Shape of Entanglement and Einstein's Equations
• Parity and the modular bootstrap
• Siegel Paramodular Forms and Sparseness in AdS${}_3$/CFT${}_2$
• Sparseness bounds on local operators in holographic $CF{T}_d$

Cited by in corpus (34)

• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• AdS Bulk Locality from Sharp CFT Bounds
• Complexity Equals Anything II
• Lorentzian CFT 3-point functions in momentum space
• Subleading Eikonal, AdS/CFT and Double Stress Tensors
• Holographic Order from Modular Chaos
• Universal Asymptotics for High Energy CFT Data
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• Probing Universalities in d>2 CFTs: from Black Holes to Shockwaves
• Gravitational path integral from the $T^2$ deformation
• Holographic OPE Coefficients from AdS Black Holes with Matters
• Looking for (and not finding) a bulk brane
• Dispersion Formulas in QFTs, CFTs, and Holography
• Light-ray operators, detectors and gravitational event shapes
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Lightcone Commutator and Stress-Tensor Exchange in $d>2$ CFTs
• On Local and Integrated Stress-Tensor Commutators
• AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering
• Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory
• Closed Strings and Weak Gravity from Higher-Spin Causality
• $d>2$ Stress-Tensor OPE near a Line
• From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT
• AdS correction to the Faddeev-Kulish state: Migrating from the Flat Peninsula
• Achronal averaged null energy condition for extremal horizons and (A)dS
• Hidden Relations of Central Charges and OPEs in Holographic CFT
• Freedom near Lightcone and ANEC Saturation
• Radiation in Fluid/Gravity and the Flat Limit
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• Conformal field theories dual to quantum gravity with strongly coupled matter
• Toward Null State Equations in $d>2$
• Resummation of Multi-Stress Tensors in Higher Dimensions
• On the Stress Tensor Light-ray Operator Algebra
• Searching for strongly coupled AdS matter with multi-trace deformations