D-instantons, Strings and M-theory

TL;DR

This paper investigates the R^4 terms in M-theory and string theories, proposing a duality-based expression that aligns with known perturbative and instanton effects, and discusses implications for non-renormalization.

Contribution

It introduces a conjecture for the R^4 terms in M-theory compactified on a torus, unifying perturbative and non-perturbative effects through duality symmetry.

Findings

The R^4 terms receive no perturbative corrections beyond one loop in ten-dimensional string theories.

The conjecture reproduces known tree-level and one-loop results accurately.

The M-theory limit includes an R^4 term from one-loop type IIA contributions.

Abstract

The R^4 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 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 corrections. This conjecture implies that the R^4 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 R^4 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)}R^4. The generalization to compactification on T^3 as well as implications for non-renormalization theorems in D-string and D-particle interactions are briefly discussed.