Lectures on Celestial Holography

Abstract

These notes consist of 3 lectures on celestial holography given at the Pre-Strings school 2021. We start by reviewing how semiclassically, the subleading soft graviton theorem implies an enhancement of the Lorentz symmetry of scattering in four-dimensional asymptotically flat gravity to Virasoro. This leads to the construction of celestial amplitudes as $\mathcal{S}$-matrices computed in a basis of boost eigenstates. Both massless and massive asymptotic states are recast as insertions on the celestial sphere transforming as global conformal primaries under the Lorentz SL$(2,\mathbb{C})$. We conclude with an overview of celestial symmetries and the constraints they impose on celestial scattering.

arXiv comment35 pages, 5 figures

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• The World as a Hologram
• The holographic principle
• New Symmetries of Massless QED
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• More Comments on String Theory on AdS_3
• Evidence for a New Soft Graviton Theorem
• Gluon Amplitudes as 2d Conformal Correlators
• A 2D Stress Tensor for 4D Gravity
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Symmetries of Celestial Amplitudes
• Null Infinity and Unitary Representation of The Poincare Group
• Strings on Celestial Sphere
• Tree-level gluon amplitudes on the celestial sphere
• Soft Photon and Graviton Theorems in Effective Field Theory
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• $(2,2)$ Scattering and the Celestial Torus
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• 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
• Conformal Blocks from Celestial Gluon Amplitudes
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• Loops on the Celestial Sphere
• Conformal properties of soft-operators - 1 : Use of null-states
• Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT
• On loop celestial amplitudes for gauge theory and gravity
• Conformal Primary Basis for Dirac Spinors
• Relativistic partial waves for celestial amplitudes
• Descendants in celestial CFT and emergent multi-collinear factorization
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• Lectures on Conformal Field Theory
• Bulk locality from the celestial amplitude
• Celestial Superamplitudes
• Magnetic Soft Charges, Dual Supertranslations and 't Hooft Line Dressings
• Quantum Gravity Phenomenology in the Infrared
• w(1+infinity) and the Celestial Sphere
• Gauge and Gravity Amplitudes on the Celestial Sphere
• Zwanziger's pairwise little group on the celestial sphere
• Celestial IR divergences and the effective action of supertranslation modes

Cited by in corpus (29)

• Lectures on Celestial Amplitudes
• Conformal Carroll Scalars with Boosts
• Energy scales and black hole pseudospectra: the structural role of the scalar product
• A BMS-invariant free scalar model
• Elements of Celestial Conformal Field Theory
• Goldilocks Modes and the Three Scattering Bases
• A Review of Gravitational Memory and BMS Frame Fixing in Numerical Relativity
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Charge and Antipodal Matching across Spatial Infinity
• Celestial Holography: Lectures on Asymptotic Symmetries
• Renormalization of conformal infinity as a stretched horizon
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Infinite $\mathrm{T}\bar{\mathrm{T}}$-like symmetries of compactified LST
• Corner symmetry and quantum geometry
• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• The $\mathcal{N}=2$ Supersymmetric $w_{1+\infty }$ Symmetry in the Two-Dimensional SYK Models
• Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• Celestial Klein Spaces
• Electromagnetic multipole expansions and the logarithmic soft photon theorem
• Asymptotic Symmetries in the TsT/$T\bar{T}$ Correspondence
• Celestial OPE blocks
• Charge algebra for non-abelian large gauge symmetries at $O(r)$
• Entanglement Rényi entropies in celestial holography
• A Note on the Analytic Structure of Celestial Amplitudes
• Celestial Feynman Rules for Scalars