Averaged Null Energy Condition from Causality

Abstract

Unitary, Lorentz-invariant quantum field theories in flat spacetime obey microcausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we show that this implies that the averaged null energy, $\int du{T}_{uu}$, must be positive. This non-local operator appears in the operator product expansion of local operators in the lightcone limit, and therefore contributes to $n$-point functions. We derive a sum rule that isolates this contribution and is manifestly positive. The argument also applies to certain higher spin operators other than the stress tensor, generating an infinite family of new constraints of the form $\int du{X}_{uuu\cdots u}\ge 0$. These lead to new inequalities for the coupling constants of spinning operators in conformal field theory, which include as special cases (but are generally stronger than) the existing constraints from the lightcone bootstrap, deep inelastic scattering, conformal collider methods, and relative entropy. We also comment on the relation to the recent derivation of the averaged null energy condition from relative entropy, and suggest a more general connection between causality and information-theoretic inequalities in QFT.

arXiv comment31+8 pages

References in corpus (35)

• A bound on chaos
• Causality, Analyticity and an IR Obstruction to UV Completion
• On Renormalization Group Flows in Four Dimensions
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Conformal collider physics: Energy and charge correlations
• Holographic c-theorems in arbitrary dimensions
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• The Analytic Bootstrap and AdS Superhorizon Locality
• Spinning Conformal Correlators
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• On the RG running of the entanglement entropy of a circle
• Seeing a c-theorem with holography
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Convexity and Liberation at Large Spin
• Null energy condition and superluminal propagation
• A Quantum Focussing Conjecture
• Theorems on gravitational time delay and related issues
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• Causality Constraints in Conformal Field Theory
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Proof of the Quantum Null Energy Condition
• A Stereoscopic Look into the Bulk
• A Proof of the Conformal Collider Bounds
• Holographic evolution of the mutual information
• Achronal averaged null energy condition
• Entropy on a null surface for interacting quantum field theories and the Bousso bound
• Holographic Proof of the Quantum Null Energy Condition
• Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law
• Multipoint correlators of conformal field theories: implications for quantum critical transport
• A holographic proof of the averaged null energy condition
• A New Spin on Causality Constraints
• Conformal Field Theories and Deep Inelastic Scattering
• The averaged null energy condition for general quantum field theories in two dimensions
• The Gravity Dual of Boundary Causality
• Wedge reflection positivity

Cited by in corpus (142)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Analyticity in Spin in Conformal Theories
• De Sitter Space and the Swampland
• Light-ray operators in conformal field theory
• A spacetime derivation of the Lorentzian OPE inversion formula
• Regular black holes with asymptotically Minkowski cores
• Weight Shifting Operators and Conformal Blocks
• Modular Hamiltonians on the null plane and the Markov property of the vacuum state
• Einstein gravity 3-point functions from conformal field theory
• A General Proof of the Quantum Null Energy Condition
• Analyzing N-point Energy Correlators Inside Jets with CMS Open Data
• Dispersive CFT Sum Rules
• Bounds for OPE coefficients on the Regge trajectory
• The 3d Stress-Tensor Bootstrap
• Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
• A modular toolkit for bulk reconstruction
• Conformal Bootstrap in the Regge Limit
• Goldstone modes and photonization for higher form symmetries
• Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• Lorentzian CFT 3-point functions in momentum space
• Light Rays, Singularities, and All That
• A perturbative perspective on self-supporting wormholes
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• Chaos in the butterfly cone
• Energy Reflection and Transmission at 2D Holographic Interfaces
• A Conformal Collider for Holographic CFTs
• Einstein gravity from ANEC correlators
• A Bound on Massive Higher Spin Particles
• Relative entropy in scattering and the S-matrix bootstrap
• Constraining Quantum Fields using Modular Theory
• Light-ray Operators and the BMS Algebra
• Energy is Entanglement
• Bootstrapping the 3d Ising Stress Tensor
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• Hyperbolic compactification of M-theory and de Sitter quantum gravity
• Distributions in CFT II. Minkowski Space
• Conformal Colliders Meet the LHC
• Three-point energy correlators and the celestial block expansion
• The Holographic Shape of Entanglement and Einstein's Equations
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• A Lower Bound on the Energy Density in Classical and Quantum Field Theories
• On the light-ray algebra in conformal field theories
• Decomposition of total stress-energy for the generalised Kiselev black hole
• Recursion relations for 5-point conformal blocks
• Light-ray operators, detectors and gravitational event shapes
• Higher Spin ANEC and the Space of CFTs
• Universal Bounds on Operator Dimensions from the Average Null Energy Condition
• The Smeared Null Energy Condition
• Spectrum of End of the World Branes in Holographic BCFTs
• Geometric Constraints from Subregion Duality Beyond the Classical Regime
• New Methods for Conformal Correlation Functions
• Thermal Stress Tensor Correlators, OPE and Holography
• Ellis Wormholes in Anti-De Sitter Space
• Renormalization of gravitational Wilson lines
• Modular energy inequalities from relative entropy
• Two Point Functions in Defect CFTs
• Swampland Conditions for Higher Derivative Couplings from CFT
• Generalizing event shapes: In search of lost collider time
• Non-Gaussianities in Collider Energy Flux
• Thermodynamic Origin of the Null Energy Condition
• The Averaged Null Energy Condition and the Black Hole Interior in String Theory
• Graviton Scattering and a Sum Rule for the c Anomaly in 4D CFT
• Real-space RG, error correction and Petz map
• Celestial Conformal Colliders
• A Survey of Black Hole Thermodynamics
• Subleading Bounds on Chaos
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• On Local and Integrated Stress-Tensor Commutators
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Thermalization, Viscosity and the Averaged Null Energy Condition
• Quantum BMS transformations in conformally flat space-times and holography
• Upper and Lower Bounds on the Integrated Null Energy in Gravity
• Differential operators for superconformal correlation functions
• Four point functions in CFT's with slightly broken higher spin symmetry
• Conformal Regge Theory at Finite Boost
• A Species or Weak-Gravity Bound for Large $N$ Gauge Theories Coupled to Gravity
• Holographic QCD and magnetic fields
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• Tunnelling and dynamical violation of the Null Energy Condition
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Conformally invariant averaged null energy condition from AdS/CFT
• Saturation of the Quantum Null Energy Condition in Far-From-Equilibrium Systems
• Global aspects of conformal symmetry and the ANEC in dS and AdS
• Instant Folded Strings and Black Fivebranes
• Lectures on Faster-than-Light Travel and Time Travel
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Towards Quantum Gravity in the Lab on Quantum Processors
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• AdS correction to the Faddeev-Kulish state: Migrating from the Flat Peninsula
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Implications of ANEC for SCFTs in four dimensions
• Quantum Information Theory of the Gravitational Anomaly
• Method of images in defect conformal field theories
• A Generalized Nachtmann Theorem in CFT
• Causality Constraints in Large $N$ QCD Coupled to Gravity
• Achronal averaged null energy condition for extremal horizons and (A)dS
• A Note on Commutation Relation in Conformal Field Theory
• A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity
• Eternal Universes
• Generalised second law beyond the semiclassical regime
• Relative Entropy in de Sitter is a Noether Charge
• Freedom near Lightcone and ANEC Saturation
• Hidden Relations of Central Charges and OPEs in Holographic CFT
• On Causality Conditions in de Sitter Spacetime
• Renormalization Group Flows, the $a$-Theorem and Conformal Bootstrap
• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions
• Factorized lightcone expansion of conformal blocks
• Radiation in Fluid/Gravity and the Flat Limit
• Operator Size for Holographic Field Theories
• The Tortoise and the Hare: A Causality Puzzle in AdS/CFT
• Chaos bound in Bershadsky-Polyakov theory
• Null energy condition violation: Tunnelling versus the Casimir effect
• Asymptotic Limit of Null Hypersurfaces
• How Much NEC Breaking Can the Universe Endure?
• Theorems for the Lightcone Bootstrap
• The averaged null energy conditions in even dimensional curved spacetimes from AdS/CFT duality
• ANEC in $\lambda {\varphi }^4$ theory
• The gravity dual of Lorentzian OPE blocks
• Regge OPE blocks and light-ray operators
• Analytic constraints on the energy-momentum tensor in conformal field theories
• Localized thermal states and negative energy
• Time Evolution after Double Trace Deformation
• Analyticity and Causality in Conformal Field Theory
• Renormalized Quantum Stress-Energy Tensor of a Nonzero Radius Cosmic String
• Quantum null energy condition in quenched 2d CFTs
• ANEC on stress-tensor states in perturbative $\lambda {\varphi }^4$ theory
• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• Open case for a closed universe
• On the Stress Tensor Light-ray Operator Algebra
• Causality, Crossing and Analyticity in Conformal Field Theories
• Generalized monodromy method in gauge/gravity duality
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Geodesically Complete Curvature-Bounce Inflation
• Conformal Rigidity from Focusing
• Revisiting the $k$-theorem with the ANEC
• PCT Theorem, Wightman Axioms and Conformal Bootstrap
• Schwarzschild Quantum Fluctuations from Regge-Wheeler Scattering
• Light cone OPE in a CFT with lowest twist scalar primary
• Numerical Relativity, Holography and the Quantum Null Energy Condition
• Higher-spin localized shocks
• Quantum Information Approaches to Quantum Gravity