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.

61 pages, 10 figures

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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