Construct the TQFTs associated with arbitrary transformable gauge groups

Construct explicitly, from first principles, the topological quantum field theories associated with topological tensor networks based on arbitrary transformable Lie groups, including theories with infinitely many anyon types.

Background

The paper constructs physical Hilbert spaces for topological tensor networks with arbitrary transformable Lie groups, extending finite-group quantum double and compact quantum-group string-net models. Although these Hilbert spaces are topological invariants and suggest TQFTs with infinitely many anyons, the authors state that the corresponding TQFTs are not generally known. They relate this unresolved issue to the difficulty of constructing non-rational or irrational TQFTs from first principles.

References

To the best of our knowledge, the explicit TQFT associated with $\Ha_{\mathrm{phys}(\Sigma)$ is not generally known for such groups.

— Entanglement entropy in topological tensor networks  (2609.10667 - Balasubramanian et al., 9 Sep 2026) in Section 2.1, “Relation to Topological Field Theory”

Settling this would require constructing the factorization map along a closed cut and repeating the analysis of Sec.~\ref{sec:algebras} for it, which we leave for future work.

— Entanglement entropy in topological tensor networks  (2609.10667 - Balasubramanian et al., 9 Sep 2026) in Section 6.1, “The quantum double model and Turaev--Viro theory”