Publication : t10/039

Eisenstein series for higher-rank groups and string theory amplitudes

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))
Miller, S.D. (Department of Mathematics Hill Center-Busch Campus Rutgers, The State University of New Jersey 110 Frelinghuysen Rd Piscataway, NJ 08854-8019)
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)
Scattering amplitudes of superstring theory are strongly constrained by the requirement that they be invariant under dualities generated by discrete subgroups, E_n(Z), of simply-laced Lie groups in the E_n series (n<= 8). In particular, expanding the four-supergraviton amplitude at low energy gives a series of higher derivative corrections to Einstein's theory, with coefficients that are automorphic functions with a rich dependence on the moduli. Boundary conditions supplied by string and supergravity perturbation theory, together with a chain of relations between successive groups in the E_n series, constrain the constant terms of these coefficients in three distinct parabolic subgroups. Using this information we are able to determine the expressions for the first two higher derivative interactions (which are BPS-protected) in terms of specific Eisenstein series. Further, we determine key features of the coefficient of the third term in the low energy expansion of the four-supergraviton amplitude (which is also BPS-protected) in the E_8 case. This is an automorphic function that satisfies an inhomogeneous Laplace equation and has constant terms in certain parabolic subgroups that contain information about all the preceding terms.
Année de publication : 2010
Revue : Commun. Numb. Theor. Phys. 4 551-596 (2010)
Preprint : arXiv:1004.0163
Langue : Anglais

Fichier(s) à télécharger :
  • publi.pdf


    Retour en haut