Evaluating one-loop string amplitudes Article Swipe
YOU?
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· 2023
· Open Access
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· DOI: https://doi.org/10.21468/scipostphys.15.3.119
· OA: W4387106850
We evaluate one-loop open-string amplitudes at finite \alpha' <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mi>′</mml:mi> </mml:mrow> </mml:math> for the first time. Our method involves a deformation of the integration contour over the modular parameter \tau <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>τ</mml:mi> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>s</mml:mi> </mml:math> and t <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>t</mml:mi> </mml:math> and directly verify long-standing conjectures about their behaviour at high energies.
