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## "Higher central charges and topological boundaries in 2+1-dimensional TQFTs", Justin Kaidi et al., 2021

*Reviewed March 23, 2024*

*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).