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<p>We investigate conformal field theories with gauge group U(<i>N</i>) at arbitrary rank <i>N</i>, 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 <i>N</i>. Using the Koszul complex of [<CitationRef CitationID="CR1">1</CitationRef>], we implement trace relations systematically via ghosts and a fermionic charge <i>Q</i><sub><i>b</i></sub>. 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 <i>N</i>. Our results provide a direct algebraic realization of the proposals which realize trace relations in the bulk as over-maximal giant gravitons [<CitationRef CitationID="CR1">1</CitationRef>–<CitationRef CitationID="CR3">3</CitationRef>] and establish analytic continuation in <i>N</i> as a powerful tool for understanding finite-<i>N</i> effects.</p>

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Gauge invariants at arbitrary N and trace relations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月22日

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  • Pawel Caputa,
  • Robert de Mello Koch

摘要

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 Qb. 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.