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.