SIGMA 22 (2026), 079, 69 pages      arXiv:2508.13759      https://doi.org/10.3842/SIGMA.2026.079

A Boundary Characterization of Turaev-Viro TQFTs

Max-Niklas Steffen and Christoph Schweigert
Department of Mathematics, University of Hamburg, AZ - Algebra and Number Theory, Bundesstraße 55,Hamburg, Germany

Received October 20, 2025, in final form August 07, 2026; Published online August 19, 2026

Abstract
We consider three-dimensional topological field theories on manifolds with boundary defects and identify explicit boundary locality conditions. We show that 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 [Faria Martins J., Meusburger C., Adv. Math. 494 (2026), 110923, 102 pages, arXiv:2410.18049] 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 TQFTs with boundary defects admit a state sum description.

Key words: TQFT; boundary theories; defects; state sum models; Dijkgraaf-Witten theory.

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