ONE-LOOP IN 11 DIMENSIONS

Four-graviton scattering in eleven-dimensional supergravity is conside red at one loop compactified on one, two and three-dimensional tori, T he dependence on the toroidal geometry determines the known perturbati ve and non-perturbative terms in the corresponding processes in type I I superstring theories in ten, nine and eight dimensions. The ultra-vi olet divergence must be regularized so that it has a precisely determi ned finite value that is consistent both with T-duality in nine dimens ions and with eleven-dimensional supersymmetry. (C) 1997 Elsevier Scie nce B.V.