On the L ∞ formulation of Chern-Simons theories
Abstract L ∞ algebras have been largely studied as algebraic frameworks in the formulation of gauge theories in which the gauge symmetries and the dynamics of the interacting theories are contained in a set of products acting on a graded vector space. On the other hand, FDAs are differential algebra...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP04(2022)142 |
| _version_ | 1827985366393552896 |
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| author | S. Salgado |
| author_facet | S. Salgado |
| author_sort | S. Salgado |
| collection | DOAJ |
| description | Abstract L ∞ algebras have been largely studied as algebraic frameworks in the formulation of gauge theories in which the gauge symmetries and the dynamics of the interacting theories are contained in a set of products acting on a graded vector space. On the other hand, FDAs are differential algebras that generalize Lie algebras by including higher-degree differential forms in their differential equations. In this article, we review the dual relation between FDAs and L ∞ algebras. We study the formulation of standard Chern-Simons theories in terms of L ∞ algebras and extend the results to FDA-based gauge theories. We focus on two cases, namely a flat (or zero-curvature) theory and a generalized Chern-Simons theory, both including high-degree differential forms as fundamental fields. |
| first_indexed | 2024-04-09T23:13:45Z |
| format | Article |
| id | doaj.art-0befad0b6f13408aa859121197dc4001 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:13:45Z |
| publishDate | 2022-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0befad0b6f13408aa859121197dc40012023-03-22T10:09:59ZengSpringerOpenJournal of High Energy Physics1029-84792022-04-012022413410.1007/JHEP04(2022)142On the L ∞ formulation of Chern-Simons theoriesS. Salgado0Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 Munich, Germany Ludwig-Maximilians-Universität MünchenAbstract L ∞ algebras have been largely studied as algebraic frameworks in the formulation of gauge theories in which the gauge symmetries and the dynamics of the interacting theories are contained in a set of products acting on a graded vector space. On the other hand, FDAs are differential algebras that generalize Lie algebras by including higher-degree differential forms in their differential equations. In this article, we review the dual relation between FDAs and L ∞ algebras. We study the formulation of standard Chern-Simons theories in terms of L ∞ algebras and extend the results to FDA-based gauge theories. We focus on two cases, namely a flat (or zero-curvature) theory and a generalized Chern-Simons theory, both including high-degree differential forms as fundamental fields.https://doi.org/10.1007/JHEP04(2022)142Chern-Simons TheoriesDifferential and Algebraic GeometryGauge Symmetry |
| spellingShingle | S. Salgado On the L ∞ formulation of Chern-Simons theories Journal of High Energy Physics Chern-Simons Theories Differential and Algebraic Geometry Gauge Symmetry |
| title | On the L ∞ formulation of Chern-Simons theories |
| title_full | On the L ∞ formulation of Chern-Simons theories |
| title_fullStr | On the L ∞ formulation of Chern-Simons theories |
| title_full_unstemmed | On the L ∞ formulation of Chern-Simons theories |
| title_short | On the L ∞ formulation of Chern-Simons theories |
| title_sort | on the l ∞ formulation of chern simons theories |
| topic | Chern-Simons Theories Differential and Algebraic Geometry Gauge Symmetry |
| url | https://doi.org/10.1007/JHEP04(2022)142 |
| work_keys_str_mv | AT ssalgado onthelformulationofchernsimonstheories |