D-INSTANTONS, STRINGS AND M-THEORY

The R-4 terms in the effective action for M-theory compactified on a t wo-torus are motivated by combining one-loop results in type II supers tring theories with the S1(2, Z) duality symmetry. The conjectured exp ression reproduces precisely the tree-level and one-loop R-4 terms in the effective action of the type II string theories compactified on a circle, together with the expected infinite sum of instanton correctio ns. This conjecture implies that the R-4 terms in ten-dimensional stri ng type II theories receive no perturbative corrections beyond one loo p and there are also no non-perturbative corrections in the ten-dimens ional IIA theory. Furthermore, the eleven-dimensional M-theory limit e xists, in which there is an R-4 term that originates entirely from the one-loop contribution in the type IIA theory and is related by supers ymmetry to the eleven-form C-(3) R-4. The generalization to compactifi cation on T-3 as well as implications for non-renormalization theorems in D-string and D-particle interactions are briefly discussed. (C) 19 97 Elsevier Science B.V.