One-loop four-graviton string amplitude at finite '

We evaluate the one-loop four-graviton scattering amplitude in type-II superstring theory exactly in ' α ′. This result is achieved by combining physical insights into the i i ε prescription in string theory with a new technical application of the Rademacher expansion of modular integrals. We provide an implementation of our formula in C++ 𝙲++ and use it to study the behavior of the amplitude at finite ' α ′ and in different kinematic regimes. Our analysis reveals a tension between explicit computations and the saddle point analysis of Gross and Mende in the high-energy limit and suggests the presence of additional saddle points.