One-loop four-graviton string amplitude at finite $\alpha'$

TL;DR

This paper computes the exact one-loop four-graviton amplitude in type-II superstring theory at finite 1, revealing new insights into high-energy behavior and saddle points through advanced mathematical techniques.

Contribution

It introduces a novel exact formula for the one-loop four-graviton amplitude at finite 1 using Rademacher expansion and implements it computationally.

Findings

Identifies a tension between explicit computations and saddle point analysis at high energy.

Suggests the existence of additional saddle points beyond known solutions.

Provides a computational tool for studying string amplitudes at finite 1.

Abstract

We evaluate the one-loop four-graviton scattering amplitude in type-II superstring theory exactly in $\alpha'$. This result is achieved by combining physical insights into the $i\varepsilon$ prescription in string theory with a new technical application of the Rademacher expansion of modular integrals. We provide an implementation of our formula in $\texttt{C++}$ and use it to study the behavior of the amplitude at finite $\alpha'$ 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.