Topological Modular Forms and the Absence of All Heterotic Global Anomalies
Topological Modular Forms and the Absence of All Heterotic Global Anomalies
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DOI：
10.1007/s00220-023-04761-2
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发表时间：
2021-08
影响因子：
2.4
通讯作者：
Yuji Tachikawa;Mayuko Yamashita
中科院分区：
文献类型：
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作者：
Yuji Tachikawa;Mayuko Yamashita
利用Segal-Stolz-Teichner猜想，我们从拓扑模形式到弦边群的安德森对偶，用某种自然变换，在数学上重新表述了杂种优势弦理论不存在全局异常的问题。我们将表明，这种自然转换消失，这意味着杂种优势的全球异常总是缺席。在这个过程中起着重要作用的事实。沿着这条路，我们还讨论了如何利用Freed和霍普金斯关于量子场论反常的结果，在Segal-Stolz-Teichner猜想下描述的扭曲。这篇论文包含了对数学家和弦理论家的单独介绍，希望使更多的读者更容易理解内容。这些部分也被清晰地划分为数学上严格的部分和不严格的部分。
We reformulate the question of the absence of global anomalies of heterotic string theory mathematically in terms of a certain natural transformation, from topological modular forms to the Anderson dual of string bordism groups, using the Segal–Stolz–Teichner conjecture. We will show that this natural transformation vanishes, implying that heterotic global anomalies are always absent. The fact thatplays an important role in the process. Along the way, we also discuss how the twists ofcan be described under the Segal–Stolz–Teichner conjecture, by using the result of Freed and Hopkins concerning anomalies of quantum field theories. The paper contains separate introductions for mathematicians and for string theorists, in the hope of making the content more accessible to a larger audience. The sections are also demarcated cleanly into mathematically rigorous parts and those which are not.