A Celestial Route to AdS Bulk Locality

Abstract

We prove a precise form of AdS bulk locality by deriving analytical two-sided bounds on bulk Wilson coefficients. Our bounds are on the Wilson coefficients themselves, rather than their ratios, as is typically found in the literature. Inspired by the Celestial amplitudes program in flat space, we perform a Celestial transform of the CFT Mellin amplitude of four identical scalars. Using the crossing symmetric dispersion relation (CSDR), we express the resulting amplitude in terms of crossing symmetric conformal partial waves. The partial waves satisy remarkable positivity properties which along with the unitarity of the CFT prove sufficient to derive the bounds. We then employ our methods in the limit of large AdS radius and recover known bounds on flat space Wilson coefficients and new bounds on their large radius corrections. We check that the planar Mellin amplitude of four stress-tensor multiplets in $\mathcal{N}=4$ SYM satisfies our bounds. Finally, using null constraints, we derive a form of low-spin dominance in AdS EFTs. We find that the low-spin dominance is strongest in flat space and weakens as we move away from flat space towards higher AdS curvature.

arXiv comment21 pages, 1 figure, accepted for publication in JHEP

References in corpus (68)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• OPE Convergence in Conformal Field Theory
• A Natural Language for AdS/CFT Correlators
• The EFT-Hedron
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• The S-matrix Bootstrap I: QFT in AdS
• New positivity bounds from full crossing symmetry
• A Mellin space approach to the conformal bootstrap
• Positivity Bounds for Scalar Theories
• Sharp Boundaries for the Swampland
• Conformal Bootstrap in Mellin Space
• Extremal Effective Field Theories
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Analyticity and Unitarity for Cosmological Correlators
• Crossing Symmetric Dispersion Relations in QFTs
• Causality constraints on corrections to Einstein gravity
• Celestial Amplitudes from UV to IR
• Where is String Theory?
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The Inflationary Wavefunction from Analyticity and Factorization
• Into the EFThedron and UV constraints from IR consistency
• BMS Symmetry of Celestial OPE
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• On the Polyakov-Mellin bootstrap
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Rigorous Bounds on Light-by-Light Scattering
• Mellin space bootstrap for global symmetry
• Causality Constraints on Gravitational Effective Field Theories
• Flux Tube S-matrix Bootstrap
• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Crossing Symmetric Dispersion Relations for Mellin Amplitudes
• AdS Virasoro-Shapiro from single-valued periods
• AdS Virasoro-Shapiro from dispersive sum rules
• Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs
• Generalized positivity bounds on chiral perturbation theory
• Relative entropy in scattering and the S-matrix bootstrap
• The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills
• Applications of dispersive sum rules: $\epsilon$-expansion and holography
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Quantum field theory and the Bieberbach conjecture
• Dual S-matrix Bootstrap I: 2D Theory
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• On the Positive Geometry of Conformal Field Theory
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• Rigorous bounds on the Analytic $S$-matrix
• QFT, EFT and GFT
• Dispersion Formulas in QFTs, CFTs, and Holography
• Where is M-theory in the space of scattering amplitudes?
• Selection rules for the S-Matrix bootstrap
• Swampland Conditions for Higher Derivative Couplings from CFT
• Froissart bound for/from CFT Mellin amplitudes
• The Low Energy Expansion for Pion-Pion Scattering and Crossing Symmetry in Dispersion Relations
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• Celestial Geometry
• Celestial insights into the S-matrix bootstrap
• Positive geometry in the diagonal limit of the conformal bootstrap
• Bounding 3d CFT correlators
• Random Field ${\varphi }^3$ Model and Parisi-Sourlas Supersymmetry
• Natural Boundaries for Scattering Amplitudes
• Positivity, low twist dominance and CSDR for CFTs
• Dispersion relations, knot polynomials and the $q$-deformed harmonic oscillator