Massive Spinning Bosons on the Celestial Sphere

TL;DR

This work extends the celestial holography program to amplitudes with massive spinning particles by constructing integral representations for massive conformal primary wave functions (CPWs) for spin-1 and spin-2 and, via a bulk-to-boundary $H_3$ propagator, generalizing to arbitrary integer spin. It introduces a spin-$s$ massive momentum operator on the celestial sphere that closes the Poincaré algebra, enabling systematic conformal-Ward and momentum-conservation constraints on two-, three-, and four-point celestial amplitudes. The authors provide explicit three-point mappings from Minkowski space with two massless scalars and a massive vector or graviton, and verify that the resulting coefficients agree with symmetry-based predictions. A completeness argument for the massive spinning CPW basis and a consistency loop with known Minkowski-to-celestial mappings solidify a robust, invertible framework for celestial amplitudes with spinning massive legs, advancing the pursuit of an underlying celestial CFT.

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.