ONE-LOOP 4-GRAVITON AMPLITUDE IN 11-DIMENSIONAL SUPERGRAVITY

We find explicit expression for the one-loop four-graviton amplitude i n eleven-dimensional supergravity compactified on a circle. Represente d in terms of the string coupling (proportional to the compactificatio n radius) it takes the form of an infinite sum of perturbative string loop corrections. We also compute the amplitude in the case of compact ification on a 2-torus, which is given by an SL(2, Z) invariant expans ion in powers of the torus area, We discuss the structure of quantum c orrections in eleven-dimensional theory and their relation to string t heory. (C) 1997 Elsevier Science B.V.