Celestial amplitudes and conformal soft theorems

Abstract

Scattering amplitudes in $d+2$ dimensions can be expressed in terms of a conformal basis, for which the S-matrix behaves as a CFT correlation function on the celestial $d$-sphere. We explain how compact expressions for the full tree-level S-matrix of gauge theory, gravity and other QFTs extend to this conformal basis, and are easily derived from ambitwistor strings. Using these formulae and their worldsheet origins, we prove various tree-level 'conformal soft theorems' in gauge theory and gravity in any dimension; these arise from limits where the scaling dimension of an external state in the scattering process takes special values. These conformally soft limits are obscure from standard methods, but they are easily derived with ambitwistor strings. Additionally, we make an identification between the residues of conformally soft vertex operator insertions in ambitwistor strings and charges generating asymptotic symmetries.

arXiv comment18+6 pages, no figures. v2: typos corrected; v3: published version

References in corpus (47)

• Aspects of the BMS/CFT correspondence
• Scattering of Massless Particles in Arbitrary Dimension
• BMS supertranslations and Weinberg's soft graviton theorem
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Projectors, Shadows, and Conformal Blocks
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Scattering Equations and KLT Orthogonality
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• Asymptotic Symmetries of Yang-Mills Theory
• A Conformal Basis for Flat Space Amplitudes
• Ambitwistor strings and the scattering equations
• A holographic reduction of Minkowski space-time
• Evidence for a New Soft Graviton Theorem
• Spinning AdS Propagators
• Gluon Amplitudes as 2d Conformal Correlators
• A 2D Stress Tensor for 4D Gravity
• Low's Subleading Soft Theorem as a Symmetry of QED
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Ambitwistor strings and the scattering equations at one loop
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• Factorization Properties of Soft Graviton Amplitudes
• Ambitwistor strings in 4-dimensions
• Conformally Soft Photons and Gravitons
• Soft sub-leading divergences in Yang-Mills amplitudes
• Subleading soft theorem in arbitrary dimension from scattering equations
• Conformally Soft Theorem in Gauge Theory
• Symmetries of Celestial Amplitudes
• Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity
• BMS Supertranslations and Memory in Four and Higher Dimensions
• Null Infinity and Unitary Representation of The Poincare Group
• Strings on Celestial Sphere
• Tree-level gluon amplitudes on the celestial sphere
• Ambitwistor strings at null infinity and subleading soft limits
• The Polynomial Form of the Scattering Equations
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• Perturbative gauge theory at null infinity
• A Worldsheet Theory for Supergravity
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• Celestial Current Algebra from Low's Subleading Soft Theorem
• Conformal properties of soft-operators - 1 : Use of null-states
• S-matrix singularities and CFT correlation functions
• Soft Limits of Yang-Mills Amplitudes and Conformal Correlators
• Field theory actions for ambitwistor string and superstring
• Ambitwistor string vertex operators on curved backgrounds
• Yang-Mills theory from the worldsheet

Cited by in corpus (84)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Asymptotic Symmetries and Celestial CFT
• 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
• Conformally Soft Theorem In Gravity
• Celestial holography meets twisted holography: 4d amplitudes from chiral correlators
• Extended BMS Algebra of Celestial CFT
• BMS Symmetry of Celestial OPE
• $(2,2)$ Scattering and the Celestial Torus
• 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 SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Double Copy for Celestial Amplitudes
• Shifting Spin on the Celestial Sphere
• BMS Flux Algebra in Celestial Holography
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Conformal Blocks from Celestial Gluon Amplitudes
• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• Primary Fields in Celestial CFT
• Lectures on Celestial Holography
• Celestial operator products from the worldsheet
• Celestial chiral algebras, colour-kinematics duality and integrability
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Loops on the Celestial Sphere
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Modified celestial amplitude in Einstein gravity
• Celestial holography on Kerr-Schild backgrounds
• Goldilocks Modes and the Three Scattering Bases
• Conformal properties of soft-operators - 1 : Use of null-states
• Ambidextrous light transforms for celestial amplitudes
• Geometric actions and flat space holography
• Celestial double copy from the worldsheet
• Dual gravitational charges and soft theorems
• On loop celestial amplitudes for gauge theory and gravity
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Conformal properties of soft operators -- 2 : Use of null-states
• Relativistic partial waves for celestial amplitudes
• Descendants in celestial CFT and emergent multi-collinear factorization
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• From Celestial Correlators to AdS, and back
• On Sugawara construction on Celestial Sphere
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• Massive Spinning Bosons on the Celestial Sphere
• The structure of IR divergences in celestial gluon amplitudes
• Celestial Locality and the Jacobi Identity
• All-order celestial OPE in the MHV sector
• Conformally Soft Fermions
• Revisiting the Shadow Stress Tensor in Celestial CFT
• Celestial Superamplitudes
• Celestial Conformal Colliders
• Shadow Celestial Amplitude
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Symmetries in Celestial CFT${}_d$
• Logarithmic Celestial Conformal Field Theory
• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Poincaré Constraints on Celestial Amplitudes
• Detector Operators for Celestial Symmetries
• The Holographic Soft $S$-Matrix in QED and Gravity
• The Grassmannian for Celestial Superamplitudes
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• $T\bar{T}$ deformed soft theorem
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• Zwanziger's pairwise little group on the celestial sphere
• $p$-Forms on the Celestial Sphere
• Asymptotic Symmetry of Four Dimensional Einstein-Yang-Mills and Einstein-Maxwell Theory
• Celestial IR divergences and the effective action of supertranslation modes
• Celestial Gluon Amplitudes from the Outside In
• Mapping SYK to the Sky
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• BMS Algebra, Double Soft Theorems, and All That
• Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• 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
• Loop corrections versus marginal deformation in celestial holography
• Fefferman-Graham and Bondi Gauges in the Fluid/Gravity Correspondence
• Celestial Holography
• A Note on the Analytic Structure of Celestial Amplitudes