In this paper we show that in perturbative string theory the genus-one contribution to formal 2-point amplitudes can be related to the genus-zero contribution to 4-point amplitudes. This is achieved by studying special linear combinations of multiple zeta values that appear as coefficients of the amplitudes. We also exploit our results to relate closed strings to open strings at genus one using Brown's single-valued projection, proving a conjecture of Broedel, Schlotterer and the second author.

中文翻译：

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属零和属一字符串振幅和特殊的多重 zeta 值

在本文中，我们表明在微扰弦理论中，对形式 2 点振幅的属一贡献可以与对 4 点振幅的属零贡献相关。这是通过研究作为振幅系数出现的多个 zeta 值的特殊线性组合来实现的。我们还利用我们的结果，使用 Brown 的单值投影将闭弦与第一属的开弦联系起来，证明了 Broedel、Schlotterer 和第二作者的猜想。