A spherical finite tensor category with a modified trace gives a finite-dimensional open-closed 3d TFT via a new handlebody invariant and the universal construction.
A boundary characterization of Turaev-Viro TQFTs
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abstract
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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Non-semisimple open-closed 3d TFT
A spherical finite tensor category with a modified trace gives a finite-dimensional open-closed 3d TFT via a new handlebody invariant and the universal construction.