Loop corrections to superstring equations of motion

We extend to the O(32) superstring our program of renormalizing string theory by cancelling BRST anomalies between different genus worldsheets. We calculate all the anomalies arising to lowest nontrivial loop order and in general background fields. At tree level, string consistency requires the background fields to satisfy equations of motion which ensure the conformal invariance of the underlying sigma model. We implement loop anomaly cancellation by adding to these equations appropriate loop-order source terms which necessarily break conformal invariance. The procedure leads to consistent loop-corrected equations of motion which can be derived from a spacetime effective action. The loop-order terms in this action incorporate a number of crucial aspects of spacetime physics, including the interaction of the photon with the graviton and the interactions of the antisymmetric tensor field with the gauge field which are responsible for spacetime gauge anomaly cancellation. We take these results as compelling evidence that loop-corrected string theory is associated with sigma models which are not conformally invariant in the usual sense. An extended version of conformal invariance, whose deep structure has yet to be uncovered, presumably incorporates string loop physics.