A Conformal Basis for Flat Space Amplitudes

Abstract

We study solutions of the Klein-Gordon, Maxwell, and linearized Einstein equations in ${\mathbb{R}}^{1,d+1}$ that transform as $d$-dimensional conformal primaries under the Lorentz group $SO(1,d+1)$. Such solutions, called conformal primary wavefunctions, are labeled by a conformal dimension $\Delta$ and a point in ${\mathbb{R}}^d$, rather than an on-shell $(d+2)$-dimensional momentum. We show that the continuum of scalar conformal primary wavefunctions on the principal continuous series $\Delta \in \frac{d}{2}+i\mathbb{R}$ of $SO(1,d+1)$ spans a complete set of normalizable solutions to the wave equation. In the massless case, with or without spin, the transition from momentum space to conformal primary wavefunctions is implemented by a Mellin transform. As a consequence of this construction, scattering amplitudes in this basis transform covariantly under $SO(1,d+1)$ as $d$-dimensional conformal correlators.

37 pages, 4 tables

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• Spinning AdS Propagators
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Cited by in corpus (180)

• Lectures on Celestial Amplitudes
• Carrollian Perspective on Celestial Holography
• Gluon Amplitudes as 2d Conformal Correlators
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Scattering Amplitudes: Celestial and Carrollian
• Bridging Carrollian and Celestial Holography
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Weight Shifting Operators and Conformal Blocks
• Asymptotic Symmetries and Celestial CFT
• Symmetries of Celestial Amplitudes
• The Holographic Nature of Null Infinity
• Celestial Amplitudes from UV to IR
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Null Infinity and Unitary Representation of The Poincare Group
• Conformally Soft Theorem In Gravity
• Tree-level gluon amplitudes on the celestial sphere
• Strings on Celestial Sphere
• Celestial holography meets twisted holography: 4d amplitudes from chiral correlators
• Extended BMS Algebra of Celestial CFT
• AdS Witten Diagrams to Carrollian Correlators
• BMS Symmetry of Celestial OPE
• $(2,2)$ Scattering and the Celestial Torus
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• Extended Super BMS Algebra of Celestial CFT
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
• Double Copy for Celestial Amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Conformal Block Expansion in Celestial CFT
• Carrollian and celestial spaces at infinity
• Shifting Spin on the Celestial Sphere
• BMS Flux Algebra in Celestial Holography
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Conformal Blocks from Celestial Gluon Amplitudes
• Loop-corrected subleading soft theorem and the celestial stress-tensor
• A $d$-Dimensional Stress Tensor for Mink${}_{d+2}$ Gravity
• Lectures on Celestial Holography
• Celestial operator products from the worldsheet
• Celestial chiral algebras, colour-kinematics duality and integrability
• Asymptotic charges from soft scalars in even dimensions
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Loops on the Celestial Sphere
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• State-Operator Correspondence in Celestial Conformal Field Theory
• On Effective Field Theories with Celestial Duals
• Elements of Celestial Conformal Field Theory
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Celestial Current Algebra from Low's Subleading Soft Theorem
• Modified celestial amplitude in Einstein gravity
• Universal Corner Symmetry and the Orbit Method for Gravity
• Conformal properties of soft-operators - 1 : Use of null-states
• Goldilocks Modes and the Three Scattering Bases
• Celestial holography on Kerr-Schild backgrounds
• Ambidextrous light transforms for celestial amplitudes
• Celestial double copy from the worldsheet
• Symmetries of free massless particles and soft theorems
• UV considerations on scattering amplitudes in a web of theories
• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• On loop celestial amplitudes for gauge theory and gravity
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Higher-Point Conformal Blocks in the Comb Channel
• Celestial Liouville Theory for Yang-Mills Amplitudes
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Conformal properties of soft operators -- 2 : Use of null-states
• Conformal Primary Basis for Dirac Spinors
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• Non-abelian infrared divergences on the celestial sphere
• Relativistic partial waves for celestial amplitudes
• Asymptotic dynamics on the worldline for spinning particles
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Descendants in celestial CFT and emergent multi-collinear factorization
• A note on the representations of $\text{SO}(1,d+1)$
• Soft Matters, or the Recursions with Massive Spinors
• Loop-level gluon OPEs in celestial holography
• On Sugawara construction on Celestial Sphere
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• Wedge Holography in Flat Space and Celestial Holography
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• One-Loop Quantum Effects in Carroll Scalars
• Four-point correlators of light-ray operators in CCFT
• Symmetry group at future null infinity I: Scalar theory
• HPS meets AMPS: How Soft Hair Dissolves the Firewall
• A Comment on Loop Corrections to the Celestial Stress Tensor
• Bulk locality from the celestial amplitude
• The structure of IR divergences in celestial gluon amplitudes
• Celestial Leaf Amplitudes
• Implications of Superrotations
• Celestial Locality and the Jacobi Identity
• A BMS-invariant free fermion model
• Celestial Superamplitudes
• Conformally Soft Fermions
• Revisiting the Shadow Stress Tensor in Celestial CFT
• Celestial Yang-Mills Amplitudes and D=4 Conformal Blocks
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Towards higher-spin holography in flat space
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• An invitation to the principal series
• Celestial Recursion
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• Celestial amplitudes in an ambidextrous basis
• Entanglement, Soft Modes, and Celestial Holography
• Logarithmic Celestial Conformal Field Theory
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Multicollinear Singularities in Celestial CFT
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Celestial Geometry
• Poincaré Constraints on Celestial Amplitudes
• Symmetry group at future null infinity II: Vector theory
• Celestial insights into the S-matrix bootstrap
• Chaos in Celestial CFT
• Efficient Rules for All Conformal Blocks
• All-order celestial OPE from on-shell recursion
• JT gravity from holographic reduction of 3D asymptotically flat spacetime
• Detector Operators for Celestial Symmetries
• Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two
• Integrable Field Theories and Their CCFT Duals
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Celestial amplitude for 2d theory
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• Minkowski Conformal Blocks and the Regge Limit for SYK-like Models
• Light transformed gluon correlators in CCFT
• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• Celestial Mellin Amplitude
• Stress tensors of 3d Carroll CFTs
• An Infrared On-Shell Action and its Implications for Soft Charge Fluctuations in Asymptotically Flat Spacetimes
• $T\bar{T}$ deformed soft theorem
• Celestial self-dual Yang-Mills theory: a new formula and the OPE limit
• Zwanziger's pairwise little group on the celestial sphere
• $p$-Forms on the Celestial Sphere
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Asymptotic Symmetry of Four Dimensional Einstein-Yang-Mills and Einstein-Maxwell Theory
• Celestial Berends-Giele current
• Leading soft theorem for multiple gravitini
• Radiation in Fluid/Gravity and the Flat Limit
• Bulk Reconstruction of Scalar Excitations in Flat${}_3$/CCFT${}_2$ and the Flat Limit from (A)dS${}_3$/CFT${}_2$
• Celestial Gluon Amplitudes from the Outside In
• Irrelevant and marginal deformed BMS field theories
• Celestial IR divergences and the effective action of supertranslation modes
• Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group
• Mapping SYK to the Sky
• Currents in Celestial CFT
• Warped Flatland
• Conformal Wave Expansions for Flat Space Amplitudes
• Multiparticle Contributions to the Celestial OPE
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Horizon causality from holographic scattering in asymptotically dS${}_3$
• $\widehat{s{l}_2}$ symmetry of ${\mathbb{R}}^{1,3}$ gravity
• A Celestial Route to AdS Bulk Locality
• Hawking flux of 4D Schwarzschild black hole with supertransition correction to second-order
• A Shorter Path to Celestial Currents
• Celestial OPE blocks
• Celestial OPEs and $w_{1+\infty }$ algebra from worldsheet in string theory
• Correlation functions at the bulk point singularity from the gravitational eikonal S-matrix
• Notes on self-dual gravity
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Loop corrections versus marginal deformation in celestial holography
• Entanglement Rényi entropies in celestial holography
• Holographic phenomenology via overlapping degrees of freedom
• Asymptotic symmetries and soft theorems in higher-dimensional gravity
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Conformal Blocks in 2d Carrollian/Galilean CFTs and Excited State Entanglement Entropy
• Quantum field theory in flat spacetime with multiple time directions
• Character of the highest weight module of BMS algebra realized on codimensional-two boundary
• Double-soft limit and celestial shadow OPE from charge bracket
• Non-abelian soft radiation data for a celestial theory
• Celestial Holography
• A Note on the Analytic Structure of Celestial Amplitudes
• The Aharony-Bergman-Jafferis-Maldacena theory on a circle
• $sl(2,\mathds{C})\times D$ symmetry and conformal primary basis for massless fields
• Celestial Regge theory
• A 4D asymptotically flat rotating black hole solution including supertraslation correction
• Modular Flow of Celestial Conformal Field Theory
• Celestial Feynman Rules for Scalars