Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity

TL;DR

This paper explores the constraints on effective interactions in type II string theory and supergravity, revealing that higher-loop contributions are tightly controlled and may be ultraviolet finite in certain dimensions.

Contribution

It establishes a connection between supergravity loop amplitudes and string theory interactions, suggesting potential finiteness of maximally extended supergravity.

Findings

No perturbative contributions beyond k string loops in IIA limit.

Genus h=k contributions determined by one-loop supergravity amplitude.

Potential ultraviolet finiteness in dimensions d < 4 + 6/h.

Abstract

This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D^2k R^4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide powerful constraints on the effective interactions. In the ten-dimensional IIA limit we find that there can be no perturbative contributions beyond k string loops (for k>0). Furthermore, the genus h=k contributions are determined exactly by the one-loop eleven-dimensional supergravity amplitude for all values of k. A plausible interpretation of these observations is that the sum of h-loop Feynman diagrams of maximally extended supergravity is less divergent than might be expected and could be ultraviolet finite in dimensions d < 4 + 6/h -- the same bound as for N=4 Yang--Mills.