One loop in eleven dimensions

TL;DR

This paper analyzes one-loop four-graviton scattering in eleven-dimensional supergravity compactified on tori, elucidating its relation to string theory perturbative and non-perturbative effects across various dimensions.

Contribution

It provides a consistent regularization of ultra-violet divergences that respects T-duality and supersymmetry, linking supergravity calculations to string theory predictions.

Findings

Dependence on toroidal geometry determines string theory terms.

Regularization maintains T-duality and supersymmetry.

Connects supergravity divergences with string theory effects.

Abstract

Four-graviton scattering in eleven-dimensional supergravity is considered at one loop compactified on one, two and three-dimensional tori. The dependence on the toroidal geometry determines the known perturbative and non-perturbative terms in the corresponding processes in type II superstring theories in ten, nine and eight dimensions. The ultra-violet divergence must be regularized so that it has a precisely determined finite value that is consistent both with T-duality in nine dimensions and with eleven-dimensional supersymmetry.