Citation: Kaidi, Justin, et al. "Higher central charges and topological boundaries in 2+ 1-dimensional TQFTs." SciPost Physics 13.3 (2022): 067.
Web: https://arxiv.org/abs/2107.13091
Tags: Physical, Boundaries/defects
This paper makes huge progress towards understand the nature of the obstructions to constructing gapped boundaries for topological phases. It is known that having vanishing chiral central charge isn't enough. In these papers, they show that even having vanishing "higher chiral central charges" is necessary, though still not sufficient. For abelian phases, they are able to find some extra invariants which give a universal condition. For non-abelian phases, the problem is still open.
Another important part of this paper is that they give a concrete relation between being doubled and admitting gapped boundary. Namely, by studying the structure of the Witt group they show that a phase admits a gapped boundary if and only if it is doubled. This once again shows that doubling is an extremely natural/important process.
This is a very good article, which contains a large amount of interesting insight. It is certainly a must read for anyone deeply interested in gapped boundaries of topological phases.
As with most big results these days, people have tried to extend it to fermionic topological order:
> You, Minyoung. "Gapped boundaries of fermionic topological orders and higher central charges." arXiv preprint arXiv:2311.01096 (2023).