Approximate treatment of noncommutative curvature in quartic matrix model
Abstract We study a Hermitian matrix model with the standard quartic potential amended by a tr(RΦ2) term for fixed external matrix R. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model — a renormalizable noncommutative field theory. T...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2023)109 |
| _version_ | 1797836720782180352 |
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| author | D. Prekrat D. Ranković N. K. Todorović-Vasović S. Kováčik J. Tekel |
| author_facet | D. Prekrat D. Ranković N. K. Todorović-Vasović S. Kováčik J. Tekel |
| author_sort | D. Prekrat |
| collection | DOAJ |
| description | Abstract We study a Hermitian matrix model with the standard quartic potential amended by a tr(RΦ2) term for fixed external matrix R. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model — a renormalizable noncommutative field theory. The extra term breaks the unitary symmetry of the action and leads, after perturbative calculation of the unitary integral, to an effective multitrace matrix model. Accompanying the analytical treatment of this multitrace approximation, we also study the model numerically by Monte Carlo simulations. The phase structure of the model is investigated, and a modified phase diagram is identified. We observe a shift of the transition line between the 1-cut and 2-cut phases of the theory that is consistent with the previous numerical simulations and also with the removal of the noncommutative phase in the Grosse-Wulkenhaar model. |
| first_indexed | 2024-04-09T15:13:29Z |
| format | Article |
| id | doaj.art-f74bb2e99d244e568d382f0f32cc2a93 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T15:13:29Z |
| publishDate | 2023-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-f74bb2e99d244e568d382f0f32cc2a932023-04-30T11:04:52ZengSpringerOpenJournal of High Energy Physics1029-84792023-01-012023113310.1007/JHEP01(2023)109Approximate treatment of noncommutative curvature in quartic matrix modelD. Prekrat0D. Ranković1N. K. Todorović-Vasović2S. Kováčik3J. Tekel4Faculty of Physics, University of BelgradeFaculty of Pharmacy, University of BelgradeFaculty of Pharmacy, University of BelgradeDepartment of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University in BratislavaDepartment of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University in BratislavaAbstract We study a Hermitian matrix model with the standard quartic potential amended by a tr(RΦ2) term for fixed external matrix R. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model — a renormalizable noncommutative field theory. The extra term breaks the unitary symmetry of the action and leads, after perturbative calculation of the unitary integral, to an effective multitrace matrix model. Accompanying the analytical treatment of this multitrace approximation, we also study the model numerically by Monte Carlo simulations. The phase structure of the model is investigated, and a modified phase diagram is identified. We observe a shift of the transition line between the 1-cut and 2-cut phases of the theory that is consistent with the previous numerical simulations and also with the removal of the noncommutative phase in the Grosse-Wulkenhaar model.https://doi.org/10.1007/JHEP01(2023)109Matrix ModelsNon-Commutative GeometryPhase Transitions |
| spellingShingle | D. Prekrat D. Ranković N. K. Todorović-Vasović S. Kováčik J. Tekel Approximate treatment of noncommutative curvature in quartic matrix model Journal of High Energy Physics Matrix Models Non-Commutative Geometry Phase Transitions |
| title | Approximate treatment of noncommutative curvature in quartic matrix model |
| title_full | Approximate treatment of noncommutative curvature in quartic matrix model |
| title_fullStr | Approximate treatment of noncommutative curvature in quartic matrix model |
| title_full_unstemmed | Approximate treatment of noncommutative curvature in quartic matrix model |
| title_short | Approximate treatment of noncommutative curvature in quartic matrix model |
| title_sort | approximate treatment of noncommutative curvature in quartic matrix model |
| topic | Matrix Models Non-Commutative Geometry Phase Transitions |
| url | https://doi.org/10.1007/JHEP01(2023)109 |
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