The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes

Abstract

The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics. The universal factorisation that occurs in these kinematic limits has been shown to be related to conservation laws associated with asymptotic, or large, gauge symmetries. This connection has led to a deeper understanding of the symmetries of gauge and gravitational theories and to a reformulation of scattering amplitudes in a basis of boost eigenstates which makes manifest the two-dimensional global conformal symmetry of the celestial sphere. The recast, or celestial, amplitudes possess many of the properties of conformal field theory correlation functions which has suggested a path towards a holographic description of asymptotically flat spacetimes. In this review we consider these interconnected developments in our understanding of soft theorems, asymptotic symmetries and conformal field theory with a focus on the structure and symmetries of the celestial amplitudes and their holographic interpretation.

arXiv comment49 pages, 3 figures, see also the overview article arXiv:2203.13011

References in corpus (243)

• The Dynamics of General Relativity
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Causality, Analyticity and an IR Obstruction to UV Completion
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• Multi-Parton Amplitudes in Gauge Theories
• Soft Hair on Black Holes
• On BMS Invariance of Gravitational Scattering
• MHV Vertices And Tree Amplitudes In Gauge Theory
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• 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
• What is the Simplest Quantum Field Theory?
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• BMS charge algebra
• Gravity as the Square of Gauge Theory
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• Black holes and the double copy
• New Symmetries of Massless QED
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Asymptotic symmetries and subleading soft graviton theorem
• 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
• New Gravitational Memories
• A holographic reduction of Minkowski space-time
• The Momentum Kernel of Gauge and Gravity Theories
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• One-Loop Splitting Amplitudes in Gauge Theory
• The EFT-Hedron
• The soft-gluon current at one-loop order
• Spinning AdS Propagators
• Effective Field Theories from Soft Limits
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• Conserved charges of the extended Bondi-Metzner-Sachs algebra
• Gluon Amplitudes as 2d Conformal Correlators
• A 2D Stress Tensor for 4D Gravity
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Factorization in One-Loop Gauge Theory
• Low's Subleading Soft Theorem as a Symmetry of QED
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Superboost transitions, refraction memory and super-Lorentz charge algebra
• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Path integral approach to eikonal and next-to-eikonal exponentiation
• On-Shell Recursion Relations for Effective Field Theories
• A Periodic Table of Effective Field Theories
• Factorization Properties of Soft Graviton Amplitudes
• Conformally Soft Photons and Gravitons
• Soft sub-leading divergences in Yang-Mills amplitudes
• Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach
• Subleading soft theorem in arbitrary dimension from scattering equations
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• Conformally Soft Theorem in Gauge Theory
• Black Hole Entropy and Soft Hair
• Celestial amplitudes and conformal soft theorems
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• The Weyl BMS group and Einstein's equations
• Type D Spacetimes and the Weyl Double Copy
• Symmetries of Celestial Amplitudes
• Shaving off Black Hole Soft Hair
• Constraining subleading soft gluon and graviton theorems
• Extended corner symmetry, charge bracket and Einstein's equations
• Recursion Relations for Conformal Blocks
• The two-loop soft current in dimensional regularization
• High energy scattering in QCD and cross singularities of Wilson loops
• More on Soft Theorems: Trees, Loops and Strings
• The Holographic Nature of Null Infinity
• Webs in multiparton scattering using the replica trick
• Subleading soft photons and large gauge transformations
• Sub-subleading soft gravitons and large diffeomorphisms
• Single soft gluon emission at two loops
• Collinear and Soft Divergences in Perturbative Quantum Gravity
• Sub-sub-leading soft-graviton theorem in arbitrary dimension
• Diagrammatic insights into next-to-soft corrections
• Magnetic Corrections to the Soft Photon Theorem
• The Double Copy of Electric-Magnetic Duality
• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• Soft Bootstrap and Supersymmetry
• Conformally Soft Theorem In Gravity
• Null Infinity and Unitary Representation of The Poincare Group
• Tree-level gluon amplitudes on the celestial sphere
• Strings on Celestial Sphere
• The Poincaré and BMS flux-balance laws with application to binary systems
• Soft Hair as a Soft Wig
• BMS Supertranslations and Not So Soft Gravitons
• Soft Photon and Graviton Theorems in Effective Field Theory
• Sub-subleading soft gravitons: New symmetries of quantum gravity?
• Extended BMS Algebra of Celestial CFT
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities
• Evolution equation for gluon Regge trajectory
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Eikonal methods applied to gravitational scattering amplitudes
• Infinities within graviton scattering amplitudes
• Perturbative gravity at null infinity
• The BMS4 algebra at spatial infinity
• Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem
• S-duality and the Double Copy
• Ambitwistor strings at null infinity and subleading soft limits
• BMS Symmetry of Celestial OPE
• Black hole memory effect
• Extended Super BMS Algebra of Celestial CFT
• Next to subleading soft-graviton theorem in arbitrary dimensions
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Soft Factorization in QED from 2D Kac-Moody Symmetry
• Large Gauge Symmetries and Asymptotic States in QED
• Asymptotic symmetries of gravity and soft theorems for massive particles
• The Asymptotic Behavior of Massless Fields and the Memory Effect
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• The Non-Abelian Exponentiation theorem for multiple Wilson lines
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• Uplifting AdS3/CFT2 to Flat Space Holography
• Double Copy for Celestial Amplitudes
• Subleading Soft Factor for String Disk Amplitudes
• Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
• Conformal Block Expansion in Celestial CFT
• Diagrammatic Exponentiation for Products of Wilson Lines
• Monodromy Relations in Higher-Loop String Amplitudes
• Shifting Spin on the Celestial Sphere
• Higher-loop amplitude monodromy relations in string and gauge theory
• Gravitational Memory in Higher Dimensions
• New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• The Soft $\mathcal{S}$-Matrix in Gravity
• A double copy for asymptotic symmetries in the self-dual sector
• Conformal Blocks from Celestial Gluon Amplitudes
• (A)dS${}_4$ in Bondi gauge
• All-Orders Singular Emission in Gauge Theories
• Infinite-Dimensional Fermionic Symmetry in Supersymmetric Gauge Theories
• Centrally extended BMS4 Lie algebroid
• Shadows and Soft Exchange in Celestial CFT
• Perturbative gauge theory at null infinity
• A Coding of Real Null Four-Momenta into World-Sheet Co-ordinates
• Primary Fields in Celestial CFT
• Soft Theorems in Superstring Theory
• Celestial operator products from the worldsheet
• Subleading Soft Theorem for Multiple Soft Gravitons
• Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions
• Loops on the Celestial Sphere
• Soft-collinear gravity
• Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• State-Operator Correspondence in Celestial Conformal Field Theory
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Residual Local Supersymmetry and the Soft Gravitino
• Conformal properties of soft-operators - 1 : Use of null-states
• On the soft limit of closed string amplitudes with massive states
• Ambidextrous light transforms for celestial amplitudes
• Asymptotic Symmetries and Weinberg's Soft Photon Theorem in Mink${}_{d+2}$
• Lectures on W algebras and W gravity
• Subleading Soft Graviton Theorem for Loop Amplitudes
• Infinite Soft Theorems from Gauge Symmetry
• Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT
• Celestial double copy from the worldsheet
• Classical Soft Graviton Theorem Rewritten
• Dual gravitational charges and soft theorems
• Symmetries of free massless particles and soft theorems
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• Soft Limits of Yang-Mills Amplitudes and Conformal Correlators
• Loop Corrected Soft Photon Theorem as a Ward Identity
• On the soft limit of open string disk amplitudes with massive states
• Asymptotic Weyl Double Copy
• Asymptotic gravitational charges
• Null to time-like infinity Green's functions for asymptotic symmetries in Minkowski spacetime
• The asymptotic structure of electromagnetism in higher spacetime dimensions
• Asymptotic structure of a massless scalar field and its dual two-form field at spatial infinity
• Subsubleading soft theorems of gravitons and dilatons in the bosonic string
• On asymptotic symmetries in higher dimensions for any spin
• Hamiltonian derivation of dual gravitational charges
• Soft gluon emission at two loops in full color
• Soft Bootstrap and Effective Field Theories
• Infinite towers of supertranslation and superrotation memories
• Conformal properties of soft operators -- 2 : Use of null-states
• Conformal Primary Basis for Dirac Spinors
• The Effective Action of Superrotation Modes
• Non-abelian infrared divergences on the celestial sphere
• Electromagnetic duality and central charge
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Asymptotic charges in massless QED revisited: A view from Spatial Infinity
• Descendants in celestial CFT and emergent multi-collinear factorization
• Monodromy relations from twisted homology
• A note on dual gravitational charges
• Double-soft graviton amplitudes and the extended BMS charge algebra
• Black Hole Memory
• Massive Celestial Fermions
• Conservation of asymptotic charges from past to future null infinity: Maxwell fields
• On Sugawara construction on Celestial Sphere
• Asymptotic Renormalization in Flat Space: Symplectic Potential and Charges of Electromagnetism
• Double-soft behavior for scalars and gluons from string theory
• Massive Spinning Bosons on the Celestial Sphere
• Double Soft Theorem for Perturbative Gravity
• Interpolating Between Asymptotic and Near Horizon Symmetries
• Invariance of Unruh and Hawking radiation under matter-induced supertranslations
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• Double Soft Limit of Graviton Amplitude from the Cachazo-He-Yuan Formalism
• Double Soft Graviton Theorems and BMS Symmetries
• Notes on the gravitational, electromagnetic and axion memory effects
• Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves
• Magnetic Soft Charges, Dual Supertranslations and 't Hooft Line Dressings
• More on gravitational memory
• Taub-NUT from the Dirac monopole
• Geodesic congruences, impulsive gravitational waves and gravitational memory
• Asymptotic symmetries and charges at spatial infinity in general relativity
• A note on electric-magnetic duality and soft charges
• Multi-soft theorems in Gauge Theory from MHV Diagrams
• New Asymptotic Conservation laws for Electromagnetism
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• The Holographic Soft $S$-Matrix in QED and Gravity
• Asymptotic Symmetries of Maxwell Theory in Arbitrary Dimensions at Spatial Infinity
• The Grassmannian for Celestial Superamplitudes
• Multi-Soft gluon limits and extended current algebras at null-infinity
• Displacement memory effect near the horizon of black holes
• Soft Photon theorem in the small negative cosmological constant limit
• Multiloop Soft Theorem for Gravitons and Dilatons in the Bosonic String
• Soft collinear effective theory for gravity
• Soft Theorems from Compactification
• Classical Soft Theorem in the AdS-Schwarzschild spacetime in small cosmological constant limit
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• On the Symmetry Foundation of Double Soft Theorems
• Bondi-Metzner-Sachs invariance and electric-magnetic duality
• Source and Response Soft Charges for Maxwell Theory on $Ad{S}_d$
• On the multiloop soft theorem of the dilaton in the bosonic string
• Generalized BMS Algebra at Timelike Infinity
• Universality of soft theorem from locality of soft vertex operators
• Super-Hawking Radiation
• Note on electromagnetic memories
• BMS Symmetry via AdS/CFT
• Asymptotic conformal symmetry at spatial infinity
• Infrared photons and asymptotic symmetries
• The BMS-like symmetry of extremal horizons

Cited by in corpus (26)

• The SAGEX Review on Scattering Amplitudes
• Celestial chiral algebras, colour-kinematics duality and integrability
• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• From Celestial Correlators to AdS, and back
• Charge and Antipodal Matching across Spatial Infinity
• A Comment on Loop Corrections to the Celestial Stress Tensor
• All-order celestial OPE in the MHV sector
• Towards higher-spin holography in flat space
• Infinite $\mathrm{T}\bar{\mathrm{T}}$-like symmetries of compactified LST
• Chiral higher-spin holography in flat space: the Flato-Fronsdal theorem and lower-point functions
• All-order celestial OPE from on-shell recursion
• Constraining higher-spin S-matrices
• Electromagnetic multipole expansions and the logarithmic soft photon theorem
• A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?
• Diamond of Infrared Equivalences in Abelian Gauge Theories
• A Celestial Route to AdS Bulk Locality
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• QED as a many-body theory of worldlines: II. All-order S-matrix formalism
• Soft Theorems and Memory Effects at Finite Temperatures
• Entanglement Rényi entropies in celestial holography
• Celestial Eikonal Amplitudes in the Near-Horizon Region
• Flat Holography & Holographic Renormalization: Scalar Field
• Null infinity as a Killing horizon
• Double soft graviton factors from the gravitational Wilson line
• Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy
• CFT reconstruction of local bulk operators in half-Minkowski space