Structure of loop space at finite N
Abstract The space of invariants for a single matrix is generated by traces containing at most N matrices per trace. We extend this analysis to multi-matrix models at finite N. Using the Molien-Weyl formula, we compute partition functions for various multi-matrix models at different N and interpret...
Saved in:
| Main Authors: | , |
|---|---|
| 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)011 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849767576444338176 |
|---|---|
| author | Robert de Mello Koch Antal Jevicki |
| author_facet | Robert de Mello Koch Antal Jevicki |
| author_sort | Robert de Mello Koch |
| collection | DOAJ |
| description | Abstract The space of invariants for a single matrix is generated by traces containing at most N matrices per trace. We extend this analysis to multi-matrix models at finite N. Using the Molien-Weyl formula, we compute partition functions for various multi-matrix models at different N and interpret them through trace relations. This allows us to identify a complete set of invariants, naturally divided into two distinct classes: primary and secondary. The full invariant ring of the multi-matrix model is reconstructed via the Hironaka decomposition, where primary invariants act freely, while secondary invariants satisfy quadratic relations. Significantly, while traces with at most N matrices are always present, we also find invariants involving more than N matrices per trace. The primary invariants correspond to perturbative degrees of freedom, whereas the secondary invariants emerge as non-trivial background structures. The growth of secondary invariants aligns with expectations from black hole entropy, suggesting deep structural connections to gravitational systems. |
| format | Article |
| id | doaj-art-88764c6583e446ddbd2ba30097eb19b5 |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-88764c6583e446ddbd2ba30097eb19b52025-08-20T03:04:08ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025614610.1007/JHEP06(2025)011Structure of loop space at finite NRobert de Mello Koch0Antal Jevicki1School of Science, Huzhou UniversityDepartment of Physics, Brown UniversityAbstract The space of invariants for a single matrix is generated by traces containing at most N matrices per trace. We extend this analysis to multi-matrix models at finite N. Using the Molien-Weyl formula, we compute partition functions for various multi-matrix models at different N and interpret them through trace relations. This allows us to identify a complete set of invariants, naturally divided into two distinct classes: primary and secondary. The full invariant ring of the multi-matrix model is reconstructed via the Hironaka decomposition, where primary invariants act freely, while secondary invariants satisfy quadratic relations. Significantly, while traces with at most N matrices are always present, we also find invariants involving more than N matrices per trace. The primary invariants correspond to perturbative degrees of freedom, whereas the secondary invariants emerge as non-trivial background structures. The growth of secondary invariants aligns with expectations from black hole entropy, suggesting deep structural connections to gravitational systems.https://doi.org/10.1007/JHEP06(2025)0111/N ExpansionAdS-CFT CorrespondenceGauge-Gravity Correspondence |
| spellingShingle | Robert de Mello Koch Antal Jevicki Structure of loop space at finite N Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Gauge-Gravity Correspondence |
| title | Structure of loop space at finite N |
| title_full | Structure of loop space at finite N |
| title_fullStr | Structure of loop space at finite N |
| title_full_unstemmed | Structure of loop space at finite N |
| title_short | Structure of loop space at finite N |
| title_sort | structure of loop space at finite n |
| topic | 1/N Expansion AdS-CFT Correspondence Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP06(2025)011 |
| work_keys_str_mv | AT robertdemellokoch structureofloopspaceatfiniten AT antaljevicki structureofloopspaceatfiniten |