Higher central charges and topological boundaries in 2+1-dimensional TQFTs
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 co...
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| Format: | Article |
| Language: | English |
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SciPost
2022-09-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.13.3.067 |
| _version_ | 1818017123422699520 |
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| author | Justin Kaidi, Zohar Komargodski, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng Shao |
| author_facet | Justin Kaidi, Zohar Komargodski, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng Shao |
| author_sort | Justin Kaidi, Zohar Komargodski, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng Shao |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T07:22:48Z |
| format | Article |
| id | doaj.art-a360984050c94f8d8928250891ecd3bd |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-14T07:22:48Z |
| publishDate | 2022-09-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-a360984050c94f8d8928250891ecd3bd2022-12-22T02:06:07ZengSciPostSciPost Physics2542-46532022-09-0113306710.21468/SciPostPhys.13.3.067Higher central charges and topological boundaries in 2+1-dimensional TQFTsJustin Kaidi, Zohar Komargodski, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng ShaoA 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.https://scipost.org/SciPostPhys.13.3.067 |
| spellingShingle | Justin Kaidi, Zohar Komargodski, Kantaro Ohmori, Sahand Seifnashri, Shu-Heng Shao Higher central charges and topological boundaries in 2+1-dimensional TQFTs SciPost Physics |
| title | Higher central charges and topological boundaries in 2+1-dimensional TQFTs |
| title_full | Higher central charges and topological boundaries in 2+1-dimensional TQFTs |
| title_fullStr | Higher central charges and topological boundaries in 2+1-dimensional TQFTs |
| title_full_unstemmed | Higher central charges and topological boundaries in 2+1-dimensional TQFTs |
| title_short | Higher central charges and topological boundaries in 2+1-dimensional TQFTs |
| title_sort | higher central charges and topological boundaries in 2 1 dimensional tqfts |
| url | https://scipost.org/SciPostPhys.13.3.067 |
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