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arXiv · 2412.17579

Closed-string amplitude recursions from the Deligne associator

Konstantin Baune·Johannes Broedel·Federico Zerbini
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Abstract

Inspired by earlier results on recursions for open-string tree-level amplitudes, and by a result of Brown and Dupont relating open- and closed-string tree-level amplitudes via single-valued periods, we identify a recursive relation for closed-string tree-level amplitudes. We achieve this by showing that closed-string analogues of Selberg integrals satisfy the Knizhnik-Zamolodchikov equation for a suitable matrix representation of the free Lie algebra on two generators, and by identifying the limits at z=1 and z=0, which are related by the Deligne associator, with N-point and (N-1)-point closed-string amplitudes, respectively.

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Konstantin Baune, Johannes Broedel, Federico Zerbini. 2024-12-23. Closed-string amplitude recursions from the Deligne associator. https://arxiv.org/abs/2412.17579

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