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

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.