Classify topological boundary conditions for continuous and non-compact groups

Classify the topological boundary conditions of the TQFTs associated with topological tensor networks whose gauge groups are continuous and possibly non-compact, including the boundary conditions relevant to factorization maps.

Background

The entropy construction depends on imposing a topological boundary condition at the factorization cut. For finite groups, such boundary conditions are classified by subgroup and cohomological data, but the paper extends the rough and smooth boundary conditions to continuous and non-compact groups only by analogy. A complete classification would determine the allowed factorization maps and the corresponding superselection sectors and area spectra.

References

The situation is much less understood for the TQFTs of Sec.~\ref{sec:themodel}, whose gauge groups are continuous and possibly non-compact. There, the topological boundary conditions have not been classified, and we will not attempt a complete classification here.

— Entanglement entropy in topological tensor networks  (2609.10667 - Balasubramanian et al., 9 Sep 2026) in Appendix A, Section A.1, “Topological boundary conditions”