Cohen, AndrewMoore, GregoryNelson, Philip CPolchinski, Joseph2023-05-232023-05-2319872017-04-16https://repository.upenn.edu/handle/20.500.14332/43301We study n-string amplitudes with one or two strings off-shell using the Polyakov path integral. The residues of the poles of these amplitudes correspond to the correct S-matrix elements. The coupling of gravitons to off-shell amplitudes shows that objects invariant under all world-sheet symmetries are also invariant under spacetime gauge symmetries. We interpret our results in terms of a local operator expansion.Physical Sciences and MathematicsPhysicsArticle