Publication : t08/100

Modular properties of two-loop maximal supergravity and connections with string 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))
Russo J.G. (Institució Catalana de Recerca i Estudis Avançats (ICREA) University of Barcelona, Av.Diagonal 647, Barcelona 08028, SPAIN)
Vanhove P. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
The low-momentum expansion of the two-loop four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a circle and a two-torus is considered up to terms of order S^6R^4 (where S is a Mandelstam invariant and R is the linearized Weyl curvature). In the case of the toroidal compactification the coefficient of each term in the low energy expansion is generically a sum of a number of SL(2,Z)-invariant functions of the complex structure of the torus. Each such function satisfies a separate Poisson equation on moduli space with particular source terms that are bilinear in coefficients of lower order terms, consistent with qualitative arguments based on supersymmetry. Comparison is made with the low-energy expansion of type II string theories in ten and nine dimensions. Although the detailed behaviour of the string amplitude is not expected to be reproduced by supergravity perturbation theory beyond certain protected terms, at the orders considered here we find a high degree of agreement with direct results from string perturbation theory. These results point to a fascinating pattern of interrelated Poisson equations for the IIB coefficients at higher orders in the momentum expansion which may have a significance beyond the particular methods by which they were motivated.
Année de publication : 2008
Revue : JHEP 0807 126 (2008)
DOI : 10.1088/1126-6708/2008/07/126
Preprint : arXiv:0807.0389
Lien :
Langue : Anglais

Fichier(s) à télécharger :
  • 1126-6708_2008_07_126.pdf
  • publi.pdf


    Retour en haut