Revisiting the Conformally Soft Sector with Celestial Diamonds

Abstract

Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.

34 pages, 2 figures

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Cited by in corpus (23)

• 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
• BMS Flux Algebra in Celestial Holography
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Gravity from symmetry: Duality and impulsive waves
• Ambidextrous light transforms for celestial amplitudes
• Goldilocks Modes and the Three Scattering Bases
• A Comment on Loop Corrections to the Celestial Stress Tensor
• Conformally Soft Fermions
• Revisiting the Shadow Stress Tensor in Celestial CFT
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial Conformal Colliders
• Celestial amplitudes in an ambidextrous basis
• Celestial Geometry
• Chaos in Celestial CFT
• $p$-Forms on the Celestial Sphere
• Celestial IR divergences and the effective action of supertranslation modes
• Mapping SYK to the Sky
• A Shorter Path to Celestial Currents