2005/10/17 by Michael B. Green, Pierre Vanhove · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/01/093
published as JHEP0601:093,2006 · harvmac. 41 pages. 3 figures. v2 typos corrected and reference list updated. v3. Significant new subsection deriving the non-zero coefficient of the IIB string theory three-loop contribution
arxiv created 2005/10/17 · arxiv updated 2009/12/01
Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D6R4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions this determines the coefficient of the D6R4 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 D6R4 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.