Evaluating one-loop string amplitudes
Lorenz Eberhardt, Sebastian Mizera
SciPost Phys. 15, 119 (2023) · published 27 September 2023
- doi: 10.21468/SciPostPhys.15.3.119
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Abstract
We evaluate one-loop open-string amplitudes at finite $\alpha'$ for the first time. Our method involves a deformation of the integration contour over the modular parameter $\tau$ to a fractal contour introduced by Rademacher in the context of analytic number theory. This procedure leads to explicit and practical formulas for the one-loop four-point amplitudes in type-I superstring theory, amenable to numerical evaluation. We plot the amplitudes as a function of the Mandelstam invariants $s$ and $t$ and directly verify long-standing conjectures about their behaviour at high energies.
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