Publication : t07/126

Low energy expansion of the four-particle genus-one amplitude in type II superstring 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, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
A diagrammatic expansion of coefficients in the low-momentum expansion of the genus-one four-particle amplitude in type II superstring theory is developed. This is applied to determine coefficients up to order s^6R^4 (where s is a Mandelstam invariant and R^4 the linearized super-curvature), and partial results are obtained beyond that order. This involves integrating powers of the scalar propagator on a toroidal world-sheet, as well as integrating over the modulus of the torus. At any given order in s the coefficients of these terms are given by rational numbers multiplying multiple zeta values (or Euler--Zagier sums) that, up to the order studied here, reduce to products of Riemann zeta values. We are careful to disentangle the analytic pieces from logarithmic threshold terms, which involves a discussion of the conditions imposed by unitarity. We further consider the compactification of the amplitude on a circle of radius r, which results in a plethora of terms that are power-behaved in r. These coefficients provide boundary `data' that must be matched by any non-perturbative expression for the low-energy expansion of the four-graviton amplitude. The paper includes an appendix by Don Zagier.
Année de publication : 2008
Revue : JHEP 0802 020 (2008)
DOI : 10.1088/1126-6708/2008/02/020
Preprint : arXiv:0801.0322
Lien :
Keywords : superstring theory; loop amplitude; S-matrix theory
Langue : Anglais

Fichier(s) à télécharger :
  • 1126-6708_2008_02_020.pdf
  • publi.pdf


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