Duality and higher derivative terms in M theory

TL;DR

This paper uses M-theory dualities and supergravity calculations to determine the exact coupling dependence of higher-derivative interactions in string theory, revealing instanton contributions and extending previous lower-order results.

Contribution

It provides the first exact determination of D^6R^4 interaction coefficients in eleven-dimensional M-theory using dualities and supergravity amplitudes, including instanton effects.

Findings

Derived the coupling dependence of D^6R^4 in M-theory.

Solved a Laplace equation for the SL(2,Z)-invariant function.

Matched perturbative string results and predicted higher-loop contributions.

Abstract

Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D^6R^4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions this determines the coefficient of the D^6R^4 interaction in eleven-dimensional M-theory. These results are obtained by considering the four-graviton two-loop scattering amplitude in eleven-dimensional supergravity compactified on a circle and on a two-torus -- extending earlier results concerning lower-derivative interactions. The torus compactification leads to an interesting SL(2,Z)-invariant function of the complex structure of the torus (the IIB string coupling) that satisfies a Laplace equation with a source term on the fundamental domain of moduli space. The structure of this equation is in accord with general supersymmetry considerations and immediately determines tree-level and one-loop contributions to D^6R^4 in perturbative IIB string theory that agree with explicit string calculations, and two-loop and three-loop contributions that have yet to be obtained in string theory. The complete solution of the Laplace equation contains infinite series' of single D-instanton and double D-instanton contributions, in addition to the perturbative terms. General considerations of the higher loop diagrams of eleven-dimensional supergravity suggest extensions of these results to interactions of higher order in the low energy expansion.