Publication : t05/123

Duality and higher derivative terms in M theory

Green M.B. (Department of Applied Mathematics and Theoretical Physics (DAMTP), Center for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England UNITED KINGDOM (UK))
Vanhove P. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
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.
Année de publication : 2006
Revue : JHEP 0601 093 (2006)
DOI : 10.1088/1126-6708/2006/01/093
Preprint : arXiv:hep-th/0510027
Lien :
PACS : 04.65.+e, 04.50.+h
Langue : Anglais

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  • 1126-6708_2006_01_093.pdf
  • publi.pdf


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