Celestial Mellin Amplitudes: Spin-1 and Spin-2 Exchange$\unicode{x2014}$and Beyond

TL;DR

This paper extends celestial Mellin amplitudes to include spin-1 and spin-2 particle exchanges, deriving explicit formulas and analyzing the operator actions in Mellin space to handle arbitrary spins.

Contribution

It introduces closed-form celestial Mellin amplitudes for spin-1 and spin-2 exchanges, including massive cases, and develops a method to incorporate arbitrary integer spins via differential operators.

Findings

Derived explicit celestial Mellin amplitudes for spin-1 and spin-2 exchanges.

Identified the celestial OPE structure for gauge bosons and gravitons.

Extended results to arbitrary integer spins using finite-difference operators.

Abstract

We further develop celestial Mellin amplitudes arXiv:2412.11992 to capture the exchange of particles with spin. For massless external scalar fields, we derive closed-form celestial Mellin amplitudes for a spin-1 and spin-2 exchange$\unicode{x2014}$both massless and massive$\unicode{x2014}$and extract the associated OPE data in the direct-channel. For gauge-boson and graviton exchanges, we identify in the celestial OPE the spin-1 current and the spin-2 stress tensor, together with the boundary gauge boson and graviton. Perturbative time-ordered correlators involving spinning fields can be obtained from those of scalars through the action of differential operators on the external points. In Mellin space these actions become finite-difference (shift) operators in the Mellin variables, which we use to extend our results to arbitrary integer spin.