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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2025)011 |
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| Summary: | 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. |
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| ISSN: | 1029-8479 |