One-loop four-graviton amplitude in eleven-dimensional supergravity

TL;DR

This paper derives the explicit one-loop four-graviton amplitude in eleven-dimensional supergravity compactified on a circle and a 2-torus, revealing its structure as an infinite sum of string loop corrections and its SL(2,Z) invariance.

Contribution

It provides the first explicit expression for the one-loop four-graviton amplitude in eleven-dimensional supergravity with compactifications, connecting quantum corrections to string theory.

Findings

Amplitude expressed as an infinite sum of string loop corrections

SL(2,Z) invariant expansion for torus compactification

Discussion of quantum correction structures in M-theory

Abstract

We find explicit expression for the one-loop four-graviton amplitude in eleven-dimensional supergravity compactified on a circle. Represented in terms of the string coupling (related to the compactification radius) it takes the form of an infinite sum of perturbative string loop corrections. We also compute the amplitude in the case of compactification on a 2-torus which is given by an SL(2,Z) invariant expansion in powers of the torus area. We discuss the structure of quantum corrections in eleven-dimensional theory and their relation to string theory.