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arXiv · 2507.22105

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

Marco Maria Baccianti·Lorenz Eberhardt·Sebastian Mizera
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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.

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Marco Maria Baccianti, Lorenz Eberhardt, Sebastian Mizera. 2025-07-29. One-loop four-graviton string amplitude at finite $\alpha'$. https://doi.org/10.21468/scipostphys.20.2.052

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