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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2507.01219 |
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| _version_ | 1866909968083451904 |
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| author | Koch, Robert de Mello Kim, Minkyoo Van Zyl, Hendrik J. R. |
| author_facet | Koch, Robert de Mello Kim, Minkyoo Van Zyl, Hendrik J. R. |
| contents | Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the module structure is determined by a finite set of secondary invariants. In this work, we show that the number of primary invariants can be computed by performing a complete gauge fixing, which identifies the number of independent physical degrees of freedom. We then compare this result to a complementary counting based on the restricted Schur polynomial basis. This comparison allows us to argue that the number of secondary invariants must exhibit exponential growth of the form $e^{cN^2}$ at large $N$, with $c$ a constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Symmetry to Structure: Gauge-Invariant Operators in Multi-Matrix Quantum Mechanics Koch, Robert de Mello Kim, Minkyoo Van Zyl, Hendrik J. R. High Energy Physics - Theory Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the module structure is determined by a finite set of secondary invariants. In this work, we show that the number of primary invariants can be computed by performing a complete gauge fixing, which identifies the number of independent physical degrees of freedom. We then compare this result to a complementary counting based on the restricted Schur polynomial basis. This comparison allows us to argue that the number of secondary invariants must exhibit exponential growth of the form $e^{cN^2}$ at large $N$, with $c$ a constant. |
| title | From Symmetry to Structure: Gauge-Invariant Operators in Multi-Matrix Quantum Mechanics |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.01219 |