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arXiv · 1912.09927

Amplitude recursions with an extra marked point

Johannes Broedel·Andre Kaderli
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Abstract

The recursive calculation of Selberg integrals by Aomoto and Terasoma using the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an auxiliary point and facilitates the recursive evaluation of string amplitudes at genus zero: open-string N-point amplitudes can be obtained from those at N-1 points. We establish a similar formalism at genus one, which allows the recursive calculation of genus-one Selberg integrals using an extra marked point in a differential equation of Knizhnik-Zamolodchikov-Bernard type. Hereby genus-one Selberg integrals are related to genus-zero Selberg integrals. Accordingly, N-point open-string amplitudes at genus one can be obtained from (N+2)-point open-string amplitudes at tree level. The construction is related to and in accordance with various recent results in intersection theory and string theory.

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Johannes Broedel, Andre Kaderli. 2019-12-20. Amplitude recursions with an extra marked point. https://doi.org/10.4310/cntp.2022.v16.n1.a3

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