A generalized 4d Chern-Simons theory
Abstract A generalization of the 4d Chern-Simons theory action introduced by Costello and Yamazaki is presented. We apply general arguments from symplectic geometry concerning the Hamiltonian action of a symmetry group on the space of gauge connections defined on a 4d manifold and construct an actio...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-11-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2023)144 |
| _version_ | 1797199688120664064 |
|---|---|
| author | David M. Schmidtt |
| author_facet | David M. Schmidtt |
| author_sort | David M. Schmidtt |
| collection | DOAJ |
| description | Abstract A generalization of the 4d Chern-Simons theory action introduced by Costello and Yamazaki is presented. We apply general arguments from symplectic geometry concerning the Hamiltonian action of a symmetry group on the space of gauge connections defined on a 4d manifold and construct an action functional that is quadratic in the moment map associated to the group action. The generalization relies on the use of contact 1-forms defined on non-trivial circle bundles over Riemann surfaces and mimics closely the approach used by Beasley and Witten to reformulate conventional 3d Chern-Simons theories on Seifert manifolds. We also show that the path integral of the generalized theory associated to integrable field theories of the PCM type, takes the canonical form of a symplectic integral over a subspace of the space of gauge connections, turning it a potential candidate for using the method of non-Abelian localization. Alternatively, this new quadratic completion of the 4d Chern-Simons theory can also be deduced in an intuitive way from manipulations similar to those used in T-duality. Further details on how to recover the original 4d Chern-Simons theory data, from the point of view of the Hamiltonian formalism applied to the generalized theory, are included as well. |
| first_indexed | 2024-03-09T15:32:21Z |
| format | Article |
| id | doaj.art-9faa5ca3780743ac8e11f4b43232fd47 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-24T07:19:43Z |
| publishDate | 2023-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9faa5ca3780743ac8e11f4b43232fd472024-04-21T11:05:52ZengSpringerOpenJournal of High Energy Physics1029-84792023-11-0120231115310.1007/JHEP11(2023)144A generalized 4d Chern-Simons theoryDavid M. Schmidtt0Departamento de Física, Universidade Federal de São CarlosAbstract A generalization of the 4d Chern-Simons theory action introduced by Costello and Yamazaki is presented. We apply general arguments from symplectic geometry concerning the Hamiltonian action of a symmetry group on the space of gauge connections defined on a 4d manifold and construct an action functional that is quadratic in the moment map associated to the group action. The generalization relies on the use of contact 1-forms defined on non-trivial circle bundles over Riemann surfaces and mimics closely the approach used by Beasley and Witten to reformulate conventional 3d Chern-Simons theories on Seifert manifolds. We also show that the path integral of the generalized theory associated to integrable field theories of the PCM type, takes the canonical form of a symplectic integral over a subspace of the space of gauge connections, turning it a potential candidate for using the method of non-Abelian localization. Alternatively, this new quadratic completion of the 4d Chern-Simons theory can also be deduced in an intuitive way from manipulations similar to those used in T-duality. Further details on how to recover the original 4d Chern-Simons theory data, from the point of view of the Hamiltonian formalism applied to the generalized theory, are included as well.https://doi.org/10.1007/JHEP11(2023)144Chern-Simons TheoriesIntegrable Field Theories |
| spellingShingle | David M. Schmidtt A generalized 4d Chern-Simons theory Journal of High Energy Physics Chern-Simons Theories Integrable Field Theories |
| title | A generalized 4d Chern-Simons theory |
| title_full | A generalized 4d Chern-Simons theory |
| title_fullStr | A generalized 4d Chern-Simons theory |
| title_full_unstemmed | A generalized 4d Chern-Simons theory |
| title_short | A generalized 4d Chern-Simons theory |
| title_sort | generalized 4d chern simons theory |
| topic | Chern-Simons Theories Integrable Field Theories |
| url | https://doi.org/10.1007/JHEP11(2023)144 |
| work_keys_str_mv | AT davidmschmidtt ageneralized4dchernsimonstheory AT davidmschmidtt generalized4dchernsimonstheory |