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arXiv · 2302.09191

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

Emil Høssjer·Philippe Mathieu·Frank Thuillier
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Abstract

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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Emil Høssjer, Philippe Mathieu, Frank Thuillier. 2023-02-17. Generalized Abelian Turaev-Viro and $\mathrm{U}\!\left(1\right)$ BF Theories. https://arxiv.org/abs/2302.09191

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