Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions
Abstract We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discre...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2023
|
| Online Access: | https://hdl.handle.net/1721.1/151138 |
| _version_ | 1811086849193541632 |
|---|---|
| author | Choi, Yichul Córdova, Clay Hsin, Po-Shen Lam, Ho T. Shao, Shu-Heng |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Choi, Yichul Córdova, Clay Hsin, Po-Shen Lam, Ho T. Shao, Shu-Heng |
| author_sort | Choi, Yichul |
| collection | MIT |
| description | Abstract
We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases,
$${\mathbb {Z}}_N$$
Z
N
gauge theories, and
$$U(1)_N$$
U
(
1
)
N
Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups,
$${{{\mathcal {N}}}}=1,$$
N
=
1
,
and
$${{{\mathcal {N}}}}=4$$
N
=
4
super Yang-Mills theories. |
| first_indexed | 2024-09-23T13:35:39Z |
| format | Article |
| id | mit-1721.1/151138 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:35:39Z |
| publishDate | 2023 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1511382024-09-18T05:12:30Z Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions Choi, Yichul Córdova, Clay Hsin, Po-Shen Lam, Ho T. Shao, Shu-Heng Massachusetts Institute of Technology. Center for Theoretical Physics Abstract We discuss a variety of codimension-one, non-invertible topological defects in general 3+1d QFTs with a discrete one-form global symmetry. These include condensation defects from higher gauging of the one-form symmetries on a codimension-one manifold, each labeled by a discrete torsion class, and duality and triality defects from gauging in half of spacetime. The universal fusion rules between these non-invertible topological defects and the one-form symmetry surface defects are determined. Interestingly, the fusion coefficients are generally not numbers, but 2+1d TQFTs, such as invertible SPT phases, $${\mathbb {Z}}_N$$ Z N gauge theories, and $$U(1)_N$$ U ( 1 ) N Chern-Simons theories. The associativity of these algebras over TQFT coefficients relies on nontrivial facts about 2+1d TQFTs. We further prove that some of these non-invertible symmetries are intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flows. Duality and triality defects are realized in many familiar gauge theories, including free Maxwell theory, non-abelian gauge theories with orthogonal gauge groups, $${{{\mathcal {N}}}}=1,$$ N = 1 , and $${{{\mathcal {N}}}}=4$$ N = 4 super Yang-Mills theories. 2023-07-20T17:47:03Z 2023-07-20T17:47:03Z 2023-05-19 2023-07-19T03:23:09Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/151138 Choi, Yichul, Córdova, Clay, Hsin, Po-Shen, Lam, Ho T. and Shao, Shu-Heng. 2023. "Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions." en https://doi.org/10.1007/s00220-023-04727-4 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Choi, Yichul Córdova, Clay Hsin, Po-Shen Lam, Ho T. Shao, Shu-Heng Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions |
| title | Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions |
| title_full | Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions |
| title_fullStr | Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions |
| title_full_unstemmed | Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions |
| title_short | Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions |
| title_sort | non invertible condensation duality and triality defects in 3 1 dimensions |
| url | https://hdl.handle.net/1721.1/151138 |
| work_keys_str_mv | AT choiyichul noninvertiblecondensationdualityandtrialitydefectsin31dimensions AT cordovaclay noninvertiblecondensationdualityandtrialitydefectsin31dimensions AT hsinposhen noninvertiblecondensationdualityandtrialitydefectsin31dimensions AT lamhot noninvertiblecondensationdualityandtrialitydefectsin31dimensions AT shaoshuheng noninvertiblecondensationdualityandtrialitydefectsin31dimensions |