We give new proofs of a global and a local property of the integrals which compute closed string theory amplitudes at genus zero. Both kinds of properties are related to the newborn theory of singlevalued periods, and our proofs provide an intuitive understanding of this relation. The global property, known in physics as the KLT formula, is a factorisation of the closed string integrals into products of pairs of open string integrals. We deduce it by identifying closed string integrals with special values of single-valued correlation functions in two dimensional conformal field theory, and by obtaining their conformal block decomposition. The local property is of number theoretical nature.We write the asymptotic expansion coefficients as multiple integrals over the complex plane of special functions known as single-valued hyperlogarithms. We develop a theory of integration of single-valued hyperlogarithms, and we use it to demonstrate that the asymptotic expansion coefficients belong to the ring of single-valued multiple zeta values.

中文翻译：

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单值超对数、相关函数和闭弦振幅

我们给出了积分的全局和局部属性的新证明，这些积分计算亏格为零的闭弦理论振幅。这两种性质都与单值周期的新生儿理论有关，我们的证明提供了对这种关系的直观理解。全局属性在物理学中称为 KLT 公式，是将闭弦积分分解为成对开弦积分的乘积。我们通过识别二维共形场论中具有单值相关函数特殊值的闭弦积分，并通过获得它们的共形块分解来推导它。局部性质具有数论性质。我们将渐近展开系数写为在称为单值超对数的特殊函数的复平面​​上的多重积分。