Celestial Diamonds: Conformal Multiplets in Celestial CFT

Abstract

We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin $s=\{0,\frac{1}{2},1,\frac{3}{2},2\}$ we classify and construct all SL(2,$\mathbb{C}$) primary descendants which are organized into 'celestial diamonds'. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,$\mathbb{C}$) conformal dimension $\Delta$ and spin $J$. Radiative conformal primary wavefunctions have $J=\pm s$ and give rise to conformally soft theorems for special values of $\Delta \in \frac{1}{2}\mathbb{Z}$. They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have $|J|\le s$. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

arXiv comment61 pages, 10 figures

References in corpus (66)

• On BMS Invariance of Gravitational Scattering
• Conformal Four Point Functions and the Operator Product Expansion
• Aspects of the BMS/CFT correspondence
• Spinning Conformal Correlators
• BMS charge algebra
• New Symmetries of Massless QED
• Projectors, Shadows, and Conformal Blocks
• Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• Asymptotic Symmetries of Yang-Mills Theory
• A Conformal Basis for Flat Space Amplitudes
• A holographic reduction of Minkowski space-time
• 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
• Low's Subleading Soft Theorem as a Symmetry of QED
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• Conformal Partial Waves: Further Mathematical Results
• Conformally Soft Photons and Gravitons
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Asymptotic Symmetries and Celestial CFT
• Symmetries of Celestial Amplitudes
• Recursion Relations for Conformal Blocks
• Sub-subleading soft gravitons and large diffeomorphisms
• Subleading soft photons and large gauge transformations
• Celestial Amplitudes from UV to IR
• Conformally Soft Theorem In Gravity
• Null Infinity and Unitary Representation of The Poincare Group
• Strings on Celestial Sphere
• Sub-subleading soft gravitons: New symmetries of quantum gravity?
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Extended BMS Algebra of Celestial CFT
• Can scalars have asymptotic symmetries?
• BMS Symmetry of Celestial OPE
• MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
• Extended Super BMS Algebra of Celestial CFT
• Soft Factorization in QED from 2D Kac-Moody Symmetry
• Uplifting AdS3/CFT2 to Flat Space Holography
• Shifting Spin on the Celestial Sphere
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Conformal Blocks from Celestial Gluon Amplitudes
• Centrally extended BMS4 Lie algebroid
• Infinite-Dimensional Fermionic Symmetry in Supersymmetric Gauge Theories
• Primary Fields in Celestial CFT
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Loops on the Celestial Sphere
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Residual Local Supersymmetry and the Soft Gravitino
• Celestial Current Algebra from Low's Subleading Soft Theorem
• Conformal properties of soft-operators - 1 : Use of null-states
• Symmetries of free massless particles and soft theorems
• Conformal properties of soft operators -- 2 : Use of null-states
• Conformal Primary Basis for Dirac Spinors
• Massive Celestial Fermions
• Massive Spinning Bosons on the Celestial Sphere
• Soft theorems in maximally supersymmetric theories
• Implications of Superrotations
• Conformally Soft Fermions
• Asymptotic Fermionic Symmetry From Soft Gravitino Theorem
• From the Lorentz Group to the Celestial Sphere
• Large gauge transformation and little group for soft photons
• The Conformal Characters

Cited by in corpus (30)

• Lectures on Celestial Amplitudes
• Scattering Amplitudes: Celestial and Carrollian
• Bridging Carrollian and Celestial Holography
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Gravity from symmetry: Duality and impulsive waves
• Lectures on Celestial Holography
• Holographic Chiral Algebra: Supersymmetry, Infinite Ward Identities, and EFTs
• Ambidextrous light transforms for celestial amplitudes
• Goldilocks Modes and the Three Scattering Bases
• From Celestial Correlators to AdS, and back
• Four-point correlators of light-ray operators in CCFT
• Celestial Holography: Lectures on Asymptotic Symmetries
• A Comment on Loop Corrections to the Celestial Stress Tensor
• Celestial Superamplitudes
• Revisiting the Shadow Stress Tensor in Celestial CFT
• Conformally Soft Fermions
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Celestial Conformal Colliders
• Celestial Recursion
• The Shadow Formalism of Galilean CFT${}_2$
• Chaos in Celestial CFT
• w(1+infinity) and the Celestial Sphere
• Celestial IR divergences and the effective action of supertranslation modes
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• A Shorter Path to Celestial Currents
• Celestial OPE blocks
• Celestial Holography