Gauge Invariants at Arbitrary $N$ and Trace Relations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915683119398912 |
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| author | Caputa, Pawel Koch, Robert de Mello |
| author_facet | Caputa, Pawel Koch, Robert de Mello |
| contents | We investigate conformal field theories with gauge group $U(N)$ at arbitrary rank $N$, focusing on the role of trace relations in determining the structure of the Hilbert space. Working in the free trace algebra without imposing relations, we identify a class of evanescent states that vanish at finite $N$. Using the Koszul complex of [1], we implement trace relations systematically via ghosts and a fermionic charge $Q_b$. This framework allows us to define and compute transition amplitudes between evanescent and physical states, which we show correspond precisely to ordinary CFT amplitudes analytically continued in $N$. Our results provide a direct algebraic realization of the proposals which realize trace relations in the bulk as over-maximal giant gravitons [1-3] and establish analytic continuation in $N$ as a powerful tool for understanding finite-$N$ effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauge Invariants at Arbitrary $N$ and Trace Relations Caputa, Pawel Koch, Robert de Mello High Energy Physics - Theory We investigate conformal field theories with gauge group $U(N)$ at arbitrary rank $N$, focusing on the role of trace relations in determining the structure of the Hilbert space. Working in the free trace algebra without imposing relations, we identify a class of evanescent states that vanish at finite $N$. Using the Koszul complex of [1], we implement trace relations systematically via ghosts and a fermionic charge $Q_b$. This framework allows us to define and compute transition amplitudes between evanescent and physical states, which we show correspond precisely to ordinary CFT amplitudes analytically continued in $N$. Our results provide a direct algebraic realization of the proposals which realize trace relations in the bulk as over-maximal giant gravitons [1-3] and establish analytic continuation in $N$ as a powerful tool for understanding finite-$N$ effects. |
| title | Gauge Invariants at Arbitrary $N$ and Trace Relations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.05834 |