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arXiv · 2509.05834

Gauge Invariants at Arbitrary $N$ and Trace Relations

Pawel Caputa·Robert de Mello Koch
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Abstract

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.

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Pawel Caputa, Robert de Mello Koch. 2025-09-06. Gauge Invariants at Arbitrary $N$ and Trace Relations. https://arxiv.org/abs/2509.05834

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