Celestial Feynman Rules for Scalars

Abstract

Off-shell celestial amplitudes with both time-like and space-like external legs are defined. The Feynman rules for scalar amplitudes, viewed as a set of recursion relations for off-shell momentum space amplitudes, are transformed to the celestial sphere using the split representation. For four-point celestial amplitudes, the Feynman expansion is shown to be equivalent to a conformal partial wave decomposition, providing an interpretation of conformal partial wave expansion coefficients as integrals over off-shell three-point structures. A conformal partial wave decomposition for a simple four-point $s$-channel massless scalar celestial amplitude is derived.

21 pages, 6 figures

References in corpus (15)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• Gluon Amplitudes as 2d Conformal Correlators
• A 2D Stress Tensor for 4D Gravity
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Conformal Partial Waves: Further Mathematical Results
• Conformally Soft Theorem in Gauge Theory
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• $(2,2)$ Scattering and the Celestial Torus
• Conformal Block Expansion in Celestial CFT
• Shifting Spin on the Celestial Sphere
• Conformal Blocks from Celestial Gluon Amplitudes
• Lectures on Celestial Holography
• Celestial OPE blocks