We prove that the parallel transport of a flat \(n-1\)-gerbe on any given target space gives rise to an n-dimensional extended homotopy quantum field theory. In case the target space is the classifying space of a finite group, we provide explicit formulae for this homotopy quantum field theory in terms of transgression. Moreover, we use the geometric theory of orbifolds to give a dimension-independent version of twisted and equivariant Dijkgraaf–Witten models. Finally, we introduce twisted equivariant Dijkgraaf–Witten theories giving us in the 3-2-1-dimensional case a new class of equivariant modular tensor categories which can be understood as twisted versions of the equivariant modular categories constructed by Maier, Nikolaus and Schweigert.

中文翻译：

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平行运输高平坦的gerbes作为扩展的同伦量子场论

我们证明了平面\（n-1 \）- gerbe在任何给定目标空间上的平行传输引起了n维扩展的同伦量子场论。如果目标空间是有限群的分类空间，那么我们将根据违规性为同伦量子场论提供明确的公式。此外，我们使用球面几何理论给出了扭曲和等变Dijkgraaf–Witten模型的尺寸无关版本。最后，我们介绍扭曲等​​变量Dijkgraaf–Witten理论，在3-2-1维情况下为我们提供了一类新的等变量模量张量类别，可以将其理解为Maier，Nikolaus和Schweigert构造的等变量模量类别的扭曲形式。