A boundary characterization of Turaev-Viro TQFTs
Quantum Algebra
2025-08-20 v1 Geometric Topology
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.
Keywords
Cite
@article{arxiv.2508.13759,
title = {A boundary characterization of Turaev-Viro TQFTs},
author = {Max-Niklas Steffen and Christoph Schweigert},
journal= {arXiv preprint arXiv:2508.13759},
year = {2025}
}