Approximate treatment of noncommutative curvature in quartic matrix model
Authors
Prekrat, Dragan
Ranković, Dragana

Todorović-Vasović, Kristina Neli

Kováčik, Samuel
Tekel, Juraj
Article (Published version)
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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.
Keywords:
Matrix Models / Non-Commutative Geometry / Phase TransitionsSource:
Journal of High Energy Physics, 2023, 1Publisher:
- Springer Science and Business Media Deutschland GmbH
Funding / projects:
- Ministry of Education, Science and Technological Development, Republic of Serbia, Grant no. 200161 (University of Belgrade, Faculty of Pharmacy) (RS-200161)
- Ministry of Education, Science and Technological Development, Republic of Serbia, Grant no. 200162 (University of Belgrade, Faculty of Physics) (RS-200162)
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PharmacyTY - JOUR AU - Prekrat, Dragan AU - Ranković, Dragana AU - Todorović-Vasović, Kristina Neli AU - Kováčik, Samuel AU - Tekel, Juraj PY - 2023 UR - https://farfar.pharmacy.bg.ac.rs/handle/123456789/4421 AB - 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. PB - Springer Science and Business Media Deutschland GmbH T2 - Journal of High Energy Physics T1 - Approximate treatment of noncommutative curvature in quartic matrix model IS - 1 DO - 10.1007/JHEP01(2023)109 ER -
@article{ author = "Prekrat, Dragan and Ranković, Dragana and Todorović-Vasović, Kristina Neli and Kováčik, Samuel and Tekel, Juraj", year = "2023", 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.", publisher = "Springer Science and Business Media Deutschland GmbH", journal = "Journal of High Energy Physics", title = "Approximate treatment of noncommutative curvature in quartic matrix model", number = "1", doi = "10.1007/JHEP01(2023)109" }
Prekrat, D., Ranković, D., Todorović-Vasović, K. N., Kováčik, S.,& Tekel, J.. (2023). Approximate treatment of noncommutative curvature in quartic matrix model. in Journal of High Energy Physics Springer Science and Business Media Deutschland GmbH.(1). https://doi.org/10.1007/JHEP01(2023)109
Prekrat D, Ranković D, Todorović-Vasović KN, Kováčik S, Tekel J. Approximate treatment of noncommutative curvature in quartic matrix model. in Journal of High Energy Physics. 2023;(1). doi:10.1007/JHEP01(2023)109 .
Prekrat, Dragan, Ranković, Dragana, Todorović-Vasović, Kristina Neli, Kováčik, Samuel, Tekel, Juraj, "Approximate treatment of noncommutative curvature in quartic matrix model" in Journal of High Energy Physics, no. 1 (2023), https://doi.org/10.1007/JHEP01(2023)109 . .