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...

Full description

Saved in:
Bibliographic Details
Main Authors: Robert de Mello Koch, Animik Ghosh, Hendrik J. R. Van Zyl
Format: Article
Language:English
Published: SpringerOpen 2025-06-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP06(2025)246
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849344853547155456
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