In this note we realise current algebra with anomalous terms in terms of a $U(1)$ gauge theory, in the space of maps $M$ from $S^1$ into a compact Lie group corresponding to the current algebra. The Wilson loop around a closed curve in $M$ is shown to be the Wess–Zumino–Witten term. This discussion enables a simple understanding of the non-Abelian anomaly in the Schrödinger picture.

中文翻译：

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当前代数、U(1) 规范理论和 Wess-Zumino-Witten 模型

在这篇笔记中，我们根据 $U(1)$ 规范理论在将 $M$ 从 $S^1$ 映射到对应于当前代数的紧李群的空间中实现了当前代数与异常项。$M$ 中围绕闭合曲线的 Wilson 循环显示为 Wess-Zumino-Witten 项。这个讨论可以简单地理解薛定谔图像中的非阿贝尔异常。