Motivic multiple zeta values and superstring amplitudes
Motivic multiple zeta values and superstring amplitudes
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Motivic 多 zeta 值和超弦振幅
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Stieberger
中科院分区：
文献类型：
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作者：
O. Schlotterer;S. Stieberger
分析了树级开环和闭环超弦振幅的结构。对于开放超弦振幅，我们发现了一种引人注目且优雅的形式，它允许人们将其 α' 展开分解为几个贡献，以解释不同类别的多个 zeta 值。这种形式通过动机多重 zeta 值的分解得到支持，即后者封装了超弦振幅的 α′ 展开。此外，由余积引起的态射将 α' 展开映射到非交换的 Hopf 代数上。该映射代表了超越函数符号的概括。就该 Hopf 代数的元素而言，α′ 展开呈现出非常简单且对称的形式，它携带了所有相关信息。有了这些结果，我们还可以将闭合超弦振幅转换为非常优雅的形式。
The structure of tree-level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows one to disentangle its α′-expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the α′-expansion of the superstring amplitude. Moreover, a morphism induced by the coproduct maps the α′-expansion onto a non-commutative Hopf algebra. This map represents a generalization of the symbol of a transcendental function. In terms of elements of this Hopf algebra the α′-expansion assumes a very simple and symmetric form, which carries all the relevant information. Equipped with these results we can also cast the closed superstring amplitude into a very elegant form.