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arXiv · 2403.04677

On finite group global and gauged $q$-form symmetries in TQFT

Manuel Furlan·Pavel Putrov
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Abstract

We describe a method to implement finite group global and gauged $q$-form symmetries into the axiomatic structure of $d$-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms decorated by cohomology classes. Namely, on a manifold with a boundary, the gauge field is considered as a class in an appropriate relative cohomology group. It is defined in a way that allows self-consistent cutting and gluing of the manifolds and involves a choice of a $(d-q-2)$-skeleton in the boundary. The method, in a sense, generalizes to arbitrary $d$ and $q$ a method that has been considered in the literature in the case of $d=3,\;q=0,1$.

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Manuel Furlan, Pavel Putrov. 2024-03-07. On finite group global and gauged $q$-form symmetries in TQFT. https://arxiv.org/abs/2403.04677

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