When trying to cast the free fermion in the framework of functorial field theory, its chiral anomaly manifests in the fact that it assigns the determinant of the Dirac operator to a top-dimensional closed spin manifold, which is not a number as expected, but an element of a complex line. In functorial field theory language, this means that the theory is twisted, which gives rise to an anomaly theory. In this paper, we give a detailed construction of this anomaly theory, as a functor that sends manifolds to infinite-dimensional Clifford algebras and bordisms to bimodules.

中文翻译：

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功能场理论中自由费米子的手性异常

当试图在函数场论的框架中铸造自由费米子时，其手性异常表现为将狄拉克算子的行列式分配给一维封闭自旋流形，这不是预期的数字，而是一个复杂线的元素。在功能场论语言中，这意味着该理论是扭曲的，这引起了异常理论。在本文中，我们给出了此异常理论的详细结构，它是将流形发送到无穷维Clifford代数而将Bordism发送到双模的函子。