arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2405.08809hep-thmath.AT
收藏

用$KO$消除8维规范反常

Giving a $KO$ to 8D Gauge Anomalies

Ethan Torres

备注：
16 pages + references
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

针对8维$\frak{N}=1$ $\frak{sp}(k)$规范理论的反常问题，构建了可抵消该反常的8维拓扑场论，其核心是利用远端D3-膜与通量膜构造拓扑算符，相关$KO/KSp$-同调类参与反常抵消。

摘要：

在文献\textit{Garcia-Etxebarria:2017crf}中，研究者发现当$k>1$时，探测$O7^+$平面的$k$个D7-膜系统会出现$\frak{sp}(k)$规范反常。这些作者随后猜想，该8维$\frak{N}=1$规范理论会与一个8维拓扑场论（TFT）耦合，使整个系统无反常，从而起到“拓扑型”Green-Schwarz机制的作用。在本短文中，我们构建了这样一个8维TFT，并证明它确实能抵消规范反常。关键步骤是利用放置在7-膜堆无穷远处的D3-膜和通量膜构造相关的拓扑算符。这类对称算符上定义有拓扑向量丛，其$KO/KSp$-同调类在反常抵消中发挥作用。

英文摘要：

In \cite{Garcia-Etxebarria:2017crf}, it was found that the system of $k$ D7-branes probing an $O7^+$-plane suffers from an $\mathfrak{sp}(k)$ gauge anomaly when $k>1$. These authors then conjectured that this 8D $\mathcal{N}=1$ gauge theory couples to an 8D topological field theory (TFT) such that the total system is anomaly-free, thus acting as a "topological" Green-Schwarz mechanism. In this note, we construct such an 8D TFT and show that it indeed cancels the gauge anomaly. The key step is to engineer the relevant topological operators from D3-branes and fluxbranes placed infinitely far away from the stack of 7-branes. Such symmetry operators have topological vector bundles defined on them whose $KO/KSp$-homology classes play a role in the anomaly cancellation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑