论文标题
物理学中的差异共同体和拓扑作用
Differential cohomology and topological actions in physics
论文作者
论文摘要
我们使用差异共同体来系统地在物理学中构建大量拓扑作用，包括Chern-Simons术语，Wess-Zumino-Novikov-witten术语和Theta术语（连续或离散）。我们介绍了一个不变的差异共同体的概念，并使用它来描述具有全球对称性的理论，并使用模棱两可的差异共同体来描述具有仪表对称性的理论。有一个自然的地图，来自doivariant到不变的差异共同体，其未能跃点检测到hooft异常，即无法测量的全局对称性。我们描述了一些简单的示例，例如量子力学，例如刚体或电荷与磁性单极相结合。我们还描述了Sigma模型的示例，例如在二维中描述非亚伯隆化的示例，为此，我们提供了对Mod-2值的本质上的玻色子描述，传统上是通过传达Majorana Fermions的双重理论来看出的。在此过程中，我们描述了对差异差分的同一个共同体的平滑结构，并证明了各种精确性和分裂特性，这些特性有助于表征地位和不变理论。
We use differential cohomology to systematically construct a large class of topological actions in physics, including Chern-Simons terms, Wess-Zumino-Novikov-Witten terms, and theta terms (continuous or discrete). We introduce a notion of invariant differential cohomology and use it to describe theories with global symmetries and we use equivariant differential cohomology to describe theories with gauge symmetries. There is a natural map from equivariant to invariant differential cohomology whose failure to surject detects 't Hooft anomalies, i.e. global symmetries which cannot be gauged. We describe a number of simple examples from quantum mechanics, such as a rigid body or an electric charge coupled to a magnetic monopole. We also describe examples of sigma models, such as those describing non-abelian bosonization in two dimensions, for which we offer an intrinsically bosonic description of the mod-2-valued 't Hooft anomaly that is traditionally seen by passing to the dual theory of Majorana fermions. Along the way, we describe a smooth structure on equivariant differential cohomology and prove various exactness and splitting properties that help with the characterization of both the equivariant and invariant theories.
