Discrete gauge anomalies and instantons
Abstract We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague d = 4 Sp(k) theories, is well-understood in terms of π 4(Sp(k)) = ℤ2, but it also has an oblique relation to the instantons, labeled by π 3(G) = ℤ, via the fermion zer...
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2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)018 |
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| author | Qiang Jia Piljin Yi |
| author_facet | Qiang Jia Piljin Yi |
| author_sort | Qiang Jia |
| collection | DOAJ |
| description | Abstract We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague d = 4 Sp(k) theories, is well-understood in terms of π 4(Sp(k)) = ℤ2, but it also has an oblique relation to the instantons, labeled by π 3(G) = ℤ, via the fermion zero mode counting. We revisit this relation and point out how SU(N) theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in d = 3. |
| format | Article |
| id | doaj-art-c8cc8163356f457e8a21b8c4757eb27d |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-c8cc8163356f457e8a21b8c4757eb27d2024-11-24T12:05:09ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024812910.1007/JHEP08(2024)018Discrete gauge anomalies and instantonsQiang Jia0Piljin Yi1School of Physics, Korea Institute for Advanced StudySchool of Physics, Korea Institute for Advanced StudyAbstract We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague d = 4 Sp(k) theories, is well-understood in terms of π 4(Sp(k)) = ℤ2, but it also has an oblique relation to the instantons, labeled by π 3(G) = ℤ, via the fermion zero mode counting. We revisit this relation and point out how SU(N) theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in d = 3.https://doi.org/10.1007/JHEP08(2024)018Anomalies in Field and String TheoriesSolitons Monopoles and Instantons |
| spellingShingle | Qiang Jia Piljin Yi Discrete gauge anomalies and instantons Journal of High Energy Physics Anomalies in Field and String Theories Solitons Monopoles and Instantons |
| title | Discrete gauge anomalies and instantons |
| title_full | Discrete gauge anomalies and instantons |
| title_fullStr | Discrete gauge anomalies and instantons |
| title_full_unstemmed | Discrete gauge anomalies and instantons |
| title_short | Discrete gauge anomalies and instantons |
| title_sort | discrete gauge anomalies and instantons |
| topic | Anomalies in Field and String Theories Solitons Monopoles and Instantons |
| url | https://doi.org/10.1007/JHEP08(2024)018 |
| work_keys_str_mv | AT qiangjia discretegaugeanomaliesandinstantons AT piljinyi discretegaugeanomaliesandinstantons |