Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap.
Abstract We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the su $$ \mathfrak{su} $$ (2), the su $$ \mathfrak...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2022)032 |
| _version_ | 1819008619944869888 |
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| author | Maxim Kurkov Patrizia Vitale |
| author_facet | Maxim Kurkov Patrizia Vitale |
| author_sort | Maxim Kurkov |
| collection | DOAJ |
| description | Abstract We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the su $$ \mathfrak{su} $$ (2), the su $$ \mathfrak{su} $$ (1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x 0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L ∞ bootstrap and with symplectic embeddings, and derive the L ∞-algebra, which underlies our model. |
| first_indexed | 2024-12-21T00:43:22Z |
| format | Article |
| id | doaj.art-bf92615a47f24c0bae9fe8e602690d98 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T00:43:22Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-bf92615a47f24c0bae9fe8e602690d982022-12-21T19:21:36ZengSpringerOpenJournal of High Energy Physics1029-84792022-01-012022111910.1007/JHEP01(2022)032Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap.Maxim Kurkov0Patrizia Vitale1Dipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. AngeloDipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. AngeloAbstract We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the su $$ \mathfrak{su} $$ (2), the su $$ \mathfrak{su} $$ (1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x 0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L ∞ bootstrap and with symplectic embeddings, and derive the L ∞-algebra, which underlies our model.https://doi.org/10.1007/JHEP01(2022)032Gauge SymmetryNon-Commutative Geometry |
| spellingShingle | Maxim Kurkov Patrizia Vitale Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap. Journal of High Energy Physics Gauge Symmetry Non-Commutative Geometry |
| title | Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap. |
| title_full | Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap. |
| title_fullStr | Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap. |
| title_full_unstemmed | Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap. |
| title_short | Four-dimensional noncommutative deformations of U(1) gauge theory and L ∞ bootstrap. |
| title_sort | four dimensional noncommutative deformations of u 1 gauge theory and l ∞ bootstrap |
| topic | Gauge Symmetry Non-Commutative Geometry |
| url | https://doi.org/10.1007/JHEP01(2022)032 |
| work_keys_str_mv | AT maximkurkov fourdimensionalnoncommutativedeformationsofu1gaugetheoryandlbootstrap AT patriziavitale fourdimensionalnoncommutativedeformationsofu1gaugetheoryandlbootstrap |