Generalized symmetries and Noether’s theorem in QFT
Abstract We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which n...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2022)304 |
| _version_ | 1798037349171462144 |
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| author | Valentin Benedetti Horacio Casini Javier M. Magán |
| author_facet | Valentin Benedetti Horacio Casini Javier M. Magán |
| author_sort | Valentin Benedetti |
| collection | DOAJ |
| description | Abstract We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether’s theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). We use these results to rederive Weinberg-Witten’s theorem within local QFT, generalizing it to massless particles in arbitrary dimensions and representations of the Lorentz group. Several examples with local twists but without Noether currents are described. We end up discussing the conditions for the strong version to hold, dynamical aspects of QFT’s with non-compact generalized symmetries, scale vs conformal invariance in QFT, connections with the Coleman-Mandula theorem and aspects of global symmetries in quantum gravity. |
| first_indexed | 2024-04-11T21:25:22Z |
| format | Article |
| id | doaj.art-e5bfd32247df4d4d8cdb4f2a2cfd2fad |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T21:25:22Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e5bfd32247df4d4d8cdb4f2a2cfd2fad2022-12-22T04:02:28ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022815610.1007/JHEP08(2022)304Generalized symmetries and Noether’s theorem in QFTValentin Benedetti0Horacio Casini1Javier M. Magán2Instituto Balseiro, Centro Atómico BarilocheInstituto Balseiro, Centro Atómico BarilocheDavid Rittenhouse Laboratory, University of PennsylvaniaAbstract We show that generalized symmetries cannot be charged under a continuous global symmetry having a Noether current. Further, only non-compact generalized symmetries can be charged under a continuous global symmetry. These results follow from a finer classification of twist operators, which naturally extends to finite group global symmetries. They unravel topological obstructions to the strong version of Noether’s theorem in QFT, even if under general conditions a global symmetry can be implemented locally by twist operators (weak version). We use these results to rederive Weinberg-Witten’s theorem within local QFT, generalizing it to massless particles in arbitrary dimensions and representations of the Lorentz group. Several examples with local twists but without Noether currents are described. We end up discussing the conditions for the strong version to hold, dynamical aspects of QFT’s with non-compact generalized symmetries, scale vs conformal invariance in QFT, connections with the Coleman-Mandula theorem and aspects of global symmetries in quantum gravity.https://doi.org/10.1007/JHEP08(2022)304Global SymmetriesWilson, ’t Hooft and Polyakov loops |
| spellingShingle | Valentin Benedetti Horacio Casini Javier M. Magán Generalized symmetries and Noether’s theorem in QFT Journal of High Energy Physics Global Symmetries Wilson, ’t Hooft and Polyakov loops |
| title | Generalized symmetries and Noether’s theorem in QFT |
| title_full | Generalized symmetries and Noether’s theorem in QFT |
| title_fullStr | Generalized symmetries and Noether’s theorem in QFT |
| title_full_unstemmed | Generalized symmetries and Noether’s theorem in QFT |
| title_short | Generalized symmetries and Noether’s theorem in QFT |
| title_sort | generalized symmetries and noether s theorem in qft |
| topic | Global Symmetries Wilson, ’t Hooft and Polyakov loops |
| url | https://doi.org/10.1007/JHEP08(2022)304 |
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