SciPost Submission Page
Higher central charges and topological boundaries in 2+1-dimensional TQFTs
by Justin Kaidi, Zohar Komargodski, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng Shao
Submission summary
| Authors (as registered SciPost users): | Kantaro Ohmori · Sahand Seifnashri |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2107.13091v2 (pdf) |
| Date accepted: | Aug. 16, 2022 |
| Date submitted: | April 5, 2022, 2:36 a.m. |
| Submitted by: | Sahand Seifnashri |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
A 2+1-dimensional topological quantum field theory (TQFT) may or may not admit topological (gapped) boundary conditions. A famous necessary, but not sufficient, condition for the existence of a topological boundary condition is that the chiral central charge $c_-$ has to vanish. In this paper, we consider conditions associated with "higher" central charges, which have been introduced recently in the math literature. In terms of these new obstructions, we identify necessary and sufficient conditions for the existence of a topological boundary in the case of bosonic, Abelian TQFTs, providing an alternative to the identification of a Lagrangian subgroup. Our proof relies on general aspects of gauging generalized global symmetries. For non-Abelian TQFTs, we give a geometric way of studying topological boundary conditions, and explain certain necessary conditions given again in terms of the higher central charges. Along the way, we find a curious duality in the partition functions of Abelian TQFTs, which begs for an explanation via the 3d-3d correspondence.
Published as SciPost Phys. 13, 067 (2022)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-8-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.13091v2, delivered 2022-08-07, doi: 10.21468/SciPost.Report.5507
Weaknesses
Report
Although equivalent conditions (i.e. Lagrangian subgroups/sub-algebras) have been discussed in the literature, the higher central charges in this work require much less computation and hence is more practically accessible. Moreover, the derivation in this work also sheds new insights on the generalized global symmetries and their gauging.
This work is original, and introduces a new concept -- higher central charge, which proves to be useful. The paper is self-contained and extremely well-written. I strongly recommend its publication.
Report #1 by Anonymous (Referee 1) on 2022-8-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.13091v2, delivered 2022-08-05, doi: 10.21468/SciPost.Report.5502
Strengths
2-The paper is systematically and coherently written with occasional examples that nicely illustrate what is going on.