Massive Spinning Bosons on the Celestial Sphere

Abstract

A natural extension of the Pasterski-Shao-Strominger (PSS) prescription is described, enabling the map of Minkowski space amplitudes with massive spinning external legs to the celestial sphere to be performed. An integral representation for the conformal primary wave function (CPW) of massive spinning bosons on the celestial sphere is derived explicitly for spin-one and -two. By analogy with the spin-zero case, the spinning bulk-to-boundary propagator on Euclidean AdS is employed to extend the massive CPW integral representation to arbitrary integer spin, and to describe the appropriate inverse transform of massive spinning CPWs back to the plane wave basis in Minkowski space. Subsequently, a massive spin-$s$ momentum operator representation on the celestial sphere is determined, and used in conjunction with known Lorentz generators to derive Poincaré symmetry constraints on generic massive spinning two-, three- and four-point celestial amplitude structures. Finally, as a consistency check, three-point Minkowski space amplitudes of two massless scalars and a spin-one or -two massive boson are explicitly mapped to the celestial sphere, and the resulting three-point function coefficients are confirmed to be in exact agreement with the results obtained from Poincaré symmetry constraints.

arXiv comment26 pages, no figures, published

References in corpus (19)

• Spinning Conformal Correlators
• Spinning AdS Propagators
• Conformally Soft Photons and Gravitons
• Celestial amplitudes and conformal soft theorems
• Symmetries of Celestial Amplitudes
• Null Infinity and Unitary Representation of The Poincare Group
• Strings on Celestial Sphere
• Tree-level gluon amplitudes on the celestial sphere
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Extended BMS Algebra of Celestial CFT
• BMS Symmetry of Celestial OPE
• Uplifting AdS3/CFT2 to Flat Space Holography
• Primary Fields in Celestial CFT
• Massive Spin-2 Scattering and Asymptotic Superluminality
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• Modified celestial amplitude in Einstein gravity
• Symmetries of free massless particles and soft theorems
• S-matrix singularities and CFT correlation functions

Cited by in corpus (18)

• Lectures on Celestial Amplitudes
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Shifting Spin on the Celestial Sphere
• Loops on the Celestial Sphere
• Celestial double copy from the worldsheet
• Conformal Primary Basis for Dirac Spinors
• Relativistic partial waves for celestial amplitudes
• Asymptotic dynamics on the worldline for spinning particles
• Soft Matters, or the Recursions with Massive Spinors
• Massive Celestial Fermions
• On Sugawara construction on Celestial Sphere
• Bulk locality from the celestial amplitude
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• $p$-Forms on the Celestial Sphere
• Celestial Berends-Giele current
• $sl(2,\mathds{C})\times D$ symmetry and conformal primary basis for massless fields