Large N optimization for multi-matrix systems
Abstract In this work we revisit the problem of solving multi-matrix systems through numerical large N methods. The framework is a collective, loop space representation which provides a constrained optimization problem, addressed through master-field minimization. This scheme applies both to multi-m...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-01-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP01(2022)168 |
| _version_ | 1819231450820509696 |
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| author | Robert de Mello Koch Antal Jevicki Xianlong Liu Kagiso Mathaba João P. Rodrigues |
| author_facet | Robert de Mello Koch Antal Jevicki Xianlong Liu Kagiso Mathaba João P. Rodrigues |
| author_sort | Robert de Mello Koch |
| collection | DOAJ |
| description | Abstract In this work we revisit the problem of solving multi-matrix systems through numerical large N methods. The framework is a collective, loop space representation which provides a constrained optimization problem, addressed through master-field minimization. This scheme applies both to multi-matrix integrals (c = 0 systems) and multi-matrix quantum mechanics (c = 1 systems). The complete fluctuation spectrum is also computable in the above scheme, and is of immediate physical relevance in the later case. The complexity (and the growth of degrees of freedom) at large N have stymied earlier attempts and in the present work we present significant improvements in this regard. The (constrained) minimization and spectrum calculations are easily achieved with close to 104 variables, giving solution to Migdal-Makeenko, and collective field equations. Considering the large number of dynamical (loop) variables and the extreme nonlinearity of the problem, high precision is obtained when confronted with solvable cases. Through numerical results presented, we prove that our scheme solves, by numerical loop space methods, the general two matrix model problem. |
| first_indexed | 2024-12-23T11:45:10Z |
| format | Article |
| id | doaj.art-7bb641b624f34bc291ea76bfa4fe35c3 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-23T11:45:10Z |
| publishDate | 2022-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-7bb641b624f34bc291ea76bfa4fe35c32022-12-21T17:48:22ZengSpringerOpenJournal of High Energy Physics1029-84792022-01-012022113810.1007/JHEP01(2022)168Large N optimization for multi-matrix systemsRobert de Mello Koch0Antal Jevicki1Xianlong Liu2Kagiso Mathaba3João P. Rodrigues4School of Science, Huzhou UniversityDepartment of Physics, Brown UniversityDepartment of Physics, Brown UniversityNational Institute for Theoretical and Computational Sciences, School of Physics and Mandelstam Institute for Theoretical Physics, University of the WitwatersrandNational Institute for Theoretical and Computational Sciences, School of Physics and Mandelstam Institute for Theoretical Physics, University of the WitwatersrandAbstract In this work we revisit the problem of solving multi-matrix systems through numerical large N methods. The framework is a collective, loop space representation which provides a constrained optimization problem, addressed through master-field minimization. This scheme applies both to multi-matrix integrals (c = 0 systems) and multi-matrix quantum mechanics (c = 1 systems). The complete fluctuation spectrum is also computable in the above scheme, and is of immediate physical relevance in the later case. The complexity (and the growth of degrees of freedom) at large N have stymied earlier attempts and in the present work we present significant improvements in this regard. The (constrained) minimization and spectrum calculations are easily achieved with close to 104 variables, giving solution to Migdal-Makeenko, and collective field equations. Considering the large number of dynamical (loop) variables and the extreme nonlinearity of the problem, high precision is obtained when confronted with solvable cases. Through numerical results presented, we prove that our scheme solves, by numerical loop space methods, the general two matrix model problem.https://doi.org/10.1007/JHEP01(2022)1681/N ExpansionDuality in Gauge Field Theories |
| spellingShingle | Robert de Mello Koch Antal Jevicki Xianlong Liu Kagiso Mathaba João P. Rodrigues Large N optimization for multi-matrix systems Journal of High Energy Physics 1/N Expansion Duality in Gauge Field Theories |
| title | Large N optimization for multi-matrix systems |
| title_full | Large N optimization for multi-matrix systems |
| title_fullStr | Large N optimization for multi-matrix systems |
| title_full_unstemmed | Large N optimization for multi-matrix systems |
| title_short | Large N optimization for multi-matrix systems |
| title_sort | large n optimization for multi matrix systems |
| topic | 1/N Expansion Duality in Gauge Field Theories |
| url | https://doi.org/10.1007/JHEP01(2022)168 |
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