Conformal Block Expansion in Celestial CFT

Abstract

The 4D 4-point scattering amplitude of massless scalars via a massive exchange is expressed in a basis of conformal primary particle wavefunctions. This celestial amplitude is expanded in a basis of 2D conformal partial waves on the unitary principal series, and then rewritten as a sum over 2D conformal blocks via contour deformation. The conformal blocks include intermediate exchanges of spinning light-ray states, as well as scalar states with positive integer conformal weights. The conformal block prefactors are found as expected to be quadratic in the celestial OPE coefficients.

28 pages, 1 figure

References in corpus (3)

• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Conformal Blocks from Celestial Gluon Amplitudes
• Soft Limits of Yang-Mills Amplitudes and Conformal Correlators

Cited by in corpus (35)

• Lectures on Celestial Amplitudes
• Bridging Carrollian and Celestial Holography
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• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Lectures on Celestial Holography
• Celestial operator products from the worldsheet
• Celestial Amplitudes as AdS-Witten Diagrams
• Ambidextrous light transforms for celestial amplitudes
• Goldilocks Modes and the Three Scattering Bases
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Black Holes in Klein Space
• From Celestial Correlators to AdS, and back
• Four-point correlators of light-ray operators in CCFT
• All-order celestial OPE in the MHV sector
• Revisiting the Shadow Stress Tensor in Celestial CFT
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial Conformal Colliders
• Shadow Celestial Amplitude
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Celestial amplitudes in an ambidextrous basis
• Celestial Recursion
• Celestial Geometry
• Celestial insights into the S-matrix bootstrap
• Chaos in Celestial CFT
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• Integrable Field Theories and Their CCFT Duals
• Celestial amplitude for 2d theory
• Light transformed gluon correlators in CCFT
• Celestial IR divergences and the effective action of supertranslation modes
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Celestial OPE blocks
• Celestial Holography
• Celestial Feynman Rules for Scalars