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arXiv 2302.09191math-phmath.MP
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广义Abel Turaev-Viro和$\mathrm{U}\!\left(1\right)$ BF理论

Generalized Abelian Turaev-Viro and $\mathrm{U}\!\left(1\right)$ BF Theories

Emil Høssjer, Philippe Mathieu, Frank Thuillier

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摘要：

我们解释了它是如何可能的研究$\mathrm{U}\!\left(1\right)$ BF理论在一个连接的封闭的定向光滑$3$ -流形的路径积分的形式感谢Deligne-Beilinson上同调。我们展示了我们如何能够直接地将定义扩展到任何维度的理论族。然后，我们扩展的定义的Turaev-Viro不变量的连通封闭导向光滑$3$ -流形的阿贝尔框架中的一个家庭的不变量在任何层面上。我们表明，这些不变量可以写成离散BF理论。我们解释了我们定义的$\mathrm{U}\!\left(1\right)$ BF理论的扩展如何与我们构造的Turaev-Viro不变量的扩展相关。

英文摘要：

We explain how it is possible to study $\mathrm{U}\!\left(1\right)$ BF theory over a connected closed oriented smooth $3$-manifold in the formalism of path integral thanks to Deligne-Beilinson cohomology. We show how we can straightforwardly extend the definition to families of theories in any dimension. We extend then the definition of the Turaev-Viro invariant of a connected closed oriented smooth $3$-manifold in an Abelian framework to a family of invariants in any dimension. We show that those invariants can be written as discrete BF theories. We explain how the extensions of $\mathrm{U}\!\left(1\right)$ BF theory we defined can be related to the extensions of Turaev-Viro invariant we constructed.

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