Higher form symmetries TFT in 6d
Abstract Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories w...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP11(2022)050 |
| _version_ | 1797865718899802112 |
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| author | Fabio Apruzzi |
| author_facet | Fabio Apruzzi |
| author_sort | Fabio Apruzzi |
| collection | DOAJ |
| description | Abstract Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d SU(p) supersymmetric gauge theories with Chern-Simons level q and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity. |
| first_indexed | 2024-04-09T23:12:40Z |
| format | Article |
| id | doaj.art-0e537c80e2564187831f1bc730ee1065 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:12:40Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0e537c80e2564187831f1bc730ee10652023-03-22T10:15:52ZengSpringerOpenJournal of High Energy Physics1029-84792022-11-0120221112010.1007/JHEP11(2022)050Higher form symmetries TFT in 6dFabio Apruzzi0Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of BernAbstract Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d SU(p) supersymmetric gauge theories with Chern-Simons level q and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity.https://doi.org/10.1007/JHEP11(2022)050Anomalies in Field and String TheoriesField Theories in Higher DimensionsGlobal SymmetriesTopological Field Theories |
| spellingShingle | Fabio Apruzzi Higher form symmetries TFT in 6d Journal of High Energy Physics Anomalies in Field and String Theories Field Theories in Higher Dimensions Global Symmetries Topological Field Theories |
| title | Higher form symmetries TFT in 6d |
| title_full | Higher form symmetries TFT in 6d |
| title_fullStr | Higher form symmetries TFT in 6d |
| title_full_unstemmed | Higher form symmetries TFT in 6d |
| title_short | Higher form symmetries TFT in 6d |
| title_sort | higher form symmetries tft in 6d |
| topic | Anomalies in Field and String Theories Field Theories in Higher Dimensions Global Symmetries Topological Field Theories |
| url | https://doi.org/10.1007/JHEP11(2022)050 |
| work_keys_str_mv | AT fabioapruzzi higherformsymmetriestftin6d |