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A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory

Kaderli, A. (2020). A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory. Journal of Physics A. doi:10.1088_1751-8121_ab9462.

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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

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Free keywords: High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Algebraic Geometry, math.AG,Mathematics, Mathematical Physics, math.MP
Abstract: The string corrections of tree-level open-string amplitudes can be described by Selberg integrals satisfying a Knizhnik-Zamolodchikov (KZ) equation. This allows for a recursion of the $\alpha'$-expansion of tree-level string corrections in the number of external states using the Drinfeld associator. While the feasibility of this recursion is well-known, we provide a mathematical description in terms of twisted de Rham theory and intersection numbers of twisted forms. In particular, this leads to purely combinatorial expressions for the matrix representation of the Lie algebra generators appearing in the KZ equation in terms of directed graphs. This, in turn, admits efficient algorithms for symbolic and numerical computations using adjacency matrices of directed graphs and is a crucial step towards analogous recursions and algorithms at higher genera.

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Dates: 2019-12-192020
Publication Status: Published online
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Identifiers: arXiv: 1912.09406
URI: http://arxiv.org/abs/1912.09406
DOI: 10.1088_1751-8121_ab9462
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Title: Journal of Physics A
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