D-instantons, strings and M-theory

The R4 terms in the effective action for M-theory compactified on a two-torus are motivated by combining one-loop results in type II superstring theories with the Sl(2, Z) duality symmetry. The conjectured expression reproduces precisely the tree-level and one-loop R4 terms in the effective action of the type II string theories compactified on a circle, together with the expected infinite sum of instanton corrections. This conjecture implies that the R4 terms in ten-dimensional string type II theories receive no perturbative corrections beyond one loop and there are also no non-perturbative corrections in the ten-dimensional IIA theory. Furthermore, the eleven-dimensional M-theory limit exists, in which there is an R4 term that originates entirely from the one-loop contribution in the type IIA theory and is related by supersymmetry to the eleven-form C(3) R4. The generalization to compactification on T3 as well as implications for non-renormalization theorems in D-string and D-particle interactions are briefly discussed.