Analysis reveals boundary locality conditions in Turaev-Viro TQFTs, suggesting consistent state sum structures.
We consider three-dimensional topological field theories on manifolds with boundary defects and identify explicit boundary locality conditions. These conditions imply a state sum construction of the given TQFT. As a consistency check, we prove that Turaev-Viro state sum models obey the boundary locality conditions. Recent progress (arXiv:2410.18049v1) in the description of defects in Dijkgraaf-Witten theories enables us to show that these theories likewise satisfy boundary locality. This directly implies that Dijkgraaf-Witten theories with boundary defects admit a state sum description.
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Steffen et al. (2025) studied this question.
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