Bosonic fortuity in vector models
Abstract We investigate the space of U(N) gauge-invariant operators in coupled matrix-vector systems at finite N, extending previous work on single matrix models. By using the Molien-Weyl formula, we compute the partition function and identify the structure of primary and secondary invariants. In sp...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)246 |
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| author | Robert de Mello Koch Animik Ghosh Hendrik J. R. Van Zyl |
| author_facet | Robert de Mello Koch Animik Ghosh Hendrik J. R. Van Zyl |
| author_sort | Robert de Mello Koch |
| collection | DOAJ |
| description | Abstract We investigate the space of U(N) gauge-invariant operators in coupled matrix-vector systems at finite N, extending previous work on single matrix models. By using the Molien-Weyl formula, we compute the partition function and identify the structure of primary and secondary invariants. In specific examples we verify, using the trace relations, that these invariants do indeed generate the complete space of gauge invariant operators. For vector models with f ≤ N species of vectors, the space is freely generated by primary invariants, while for f > N, secondary invariants appear, reflecting the presence of nontrivial trace relations. We derive analytic expressions for the number of secondary invariants and explore their growth. These results suggest a bosonic analogue of the fortuity mechanism. Our findings have implications for higher-spin holography and gauge-gravity duality, with applications to both vector and matrix models. |
| format | Article |
| id | doaj-art-44b34e575c844f9e80a3b08a9c06cb80 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-44b34e575c844f9e80a3b08a9c06cb802025-08-20T03:42:34ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025611810.1007/JHEP06(2025)246Bosonic fortuity in vector modelsRobert de Mello Koch0Animik Ghosh1Hendrik J. R. Van Zyl2School of Science, Huzhou UniversitySchool of Science, Huzhou UniversityThe Laboratory for Quantum Gravity & Strings, Department of Mathematics & Applied Mathematics, University of Cape TownAbstract We investigate the space of U(N) gauge-invariant operators in coupled matrix-vector systems at finite N, extending previous work on single matrix models. By using the Molien-Weyl formula, we compute the partition function and identify the structure of primary and secondary invariants. In specific examples we verify, using the trace relations, that these invariants do indeed generate the complete space of gauge invariant operators. For vector models with f ≤ N species of vectors, the space is freely generated by primary invariants, while for f > N, secondary invariants appear, reflecting the presence of nontrivial trace relations. We derive analytic expressions for the number of secondary invariants and explore their growth. These results suggest a bosonic analogue of the fortuity mechanism. Our findings have implications for higher-spin holography and gauge-gravity duality, with applications to both vector and matrix models.https://doi.org/10.1007/JHEP06(2025)246Matrix ModelsBlack Holes in String Theory |
| spellingShingle | Robert de Mello Koch Animik Ghosh Hendrik J. R. Van Zyl Bosonic fortuity in vector models Journal of High Energy Physics Matrix Models Black Holes in String Theory |
| title | Bosonic fortuity in vector models |
| title_full | Bosonic fortuity in vector models |
| title_fullStr | Bosonic fortuity in vector models |
| title_full_unstemmed | Bosonic fortuity in vector models |
| title_short | Bosonic fortuity in vector models |
| title_sort | bosonic fortuity in vector models |
| topic | Matrix Models Black Holes in String Theory |
| url | https://doi.org/10.1007/JHEP06(2025)246 |
| work_keys_str_mv | AT robertdemellokoch bosonicfortuityinvectormodels AT animikghosh bosonicfortuityinvectormodels AT hendrikjrvanzyl bosonicfortuityinvectormodels |