The low energy expansion of the one-loop type II superstring amplitude

TL;DR

This paper computes the low energy expansion of the one-loop four-graviton amplitude in type II superstring theories, revealing coefficients consistent with duality predictions between string theory and supergravity.

Contribution

It provides explicit calculations of the amplitude expansion up to order s^4 log s R^4, connecting string theory results with supergravity expectations.

Findings

Coefficients match duality-based predictions

Expansion includes terms up to order s^4 log s R^4

Method involves integrating scalar propagator powers over the torus

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 R^4, where 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.