From Celestial Correlators to AdS, and back

Abstract

We present a general relation between celestial correlation functions in $d$-dimensions and Witten diagrams in $\left(d+1\right)$-dimensional Euclidean anti-de Sitter (EAdS) space, to all orders in perturbation theory. Contact diagram processes are proportional to contact Witten diagrams, and particle exchanges can be recast as a continuum of particle exchanges in EAdS where the exchanged particles carrying unitary Principal Series representations of $SO\left(d+1,1\right)$. One can then try to import familiar EAdS techniques to study the properties of celestial correlators. In this work we use this relation to infer the analytic structure of the spectral density in the conformal partial wave expansion of celestial correlators which, at least perturbatively, should be a meromorphic function of the spectral parameter. We also discuss non-perturbative constraints from unitarity in Euclidean Conformal Field Theory, which requires positivity of the spectral density. This extends similar relations recently uncovered between boundary correlation functions in de Sitter space and Witten diagrams in EAdS, suggesting that EAdS could play a central role in efforts towards holography for all lambdas.

arXiv comment25 pages + appendices, 5 figures

References in corpus (54)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning Conformal Correlators
• Analyticity in Spin in Conformal Theories
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Conformal Regge theory
• Graviton exchange and complete 4-point functions in the AdS/CFT correspondence
• Implications of conformal invariance in momentum space
• A holographic reduction of Minkowski space-time
• A Natural Language for AdS/CFT Correlators
• Lectures on Celestial Amplitudes
• Spinning AdS Propagators
• A 2D Stress Tensor for 4D Gravity
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• Bootstrapping Inflationary Correlators in Mellin Space
• Conformally Soft Photons and Gravitons
• A Mellin Space Approach to Cosmological Correlators
• Analyticity and Unitarity for Cosmological Correlators
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Asymptotic Symmetries and Celestial CFT
• Symmetries of Celestial Amplitudes
• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• From dS to AdS and back
• Dissipative effects in the Effective Field Theory of Inflation
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Conformally Soft Theorem In Gravity
• Strings on Celestial Sphere
• Extended BMS Algebra of Celestial CFT
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• On Squeezed Limits in Single-Field Inflation - Part I
• BMS Symmetry of Celestial OPE
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Extended Super BMS Algebra of Celestial CFT
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Double Copy for Celestial Amplitudes
• Conformal Block Expansion in Celestial CFT
• Shifting Spin on the Celestial Sphere
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• The group approach to AdS space propagators
• Celestial Amplitudes as AdS-Witten Diagrams
• Non-Gaussianity from Excited Initial Inflationary States
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Goldilocks Modes and the Three Scattering Bases
• On Sugawara construction on Celestial Sphere
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• A Comment on Loop Corrections to the Celestial Stress Tensor
• TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions
• On the consistency of (partially-)massless matter couplings in de Sitter space

Cited by in corpus (7)

• Celestial Leaf Amplitudes
• Entanglement, Soft Modes, and Celestial Holography
• Flat limit of AdS/CFT from AdS geodesics: scattering amplitudes and antipodal matching of Liénard-Wiechert fields
• Entanglement Rényi entropies in celestial holography
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Flat Holography & Holographic Renormalization: Scalar Field
• Quantum field theory in flat spacetime with multiple time directions