Celestial closed strings at one-loop

Abstract: In this paper we continue our investigation of superstring scattering amplitudes in the conformal basis. We focus on the case of four graviton scattering processes at 1-loop in \emph{closed} superstring theory. We write the expression for such a process in the celestial variables and confirm previous expectations. In particular, we find the adequate overall factorization of the $\alpha'$ dependence which organizes the loop expansion of closed string celestial amplitudes. We also show that, at 1-loop, the field theory limit, when properly defined, commutes with the Mellin transform of the amplitudes for all values of the conformally invariant cross-ratio, something that had already been observed for gluon processes at 1-loop in open string theory and is to be compared with the tree-level computations. This indicates that many of the features satisfied for open string gluon amplitudes at tree and 1-loop levels are also universal properties of graviton celestial amplitudes in closed string theory. As a by-product, we also compute field theory graviton amplitudes at 1-loop in the conformal basis.