Publication : t99/071

Abstract:
The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order $s^4 \,\log s\,{\cal R}^4$, where ${\cal R}^4$ denotes a specific contraction of four linearized Weyl tensors and $s$ is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.