有限N算子代数与双局域全息术的希尔伯特空间
Finite-$N$ Operator Algebras and the Hilbert Space of Bilocal Holography
浏览论文内容
中文总结 AI 辅助
对有限N双局域全息术的希尔伯特空间进行算子代数和表示理论描述，建立不变对偶对算子代数，证明有限N迹关系成为所选不可约表示的表示理论恒等式，总结相关情况并计算单态卡西米尔量。
中文摘要 AI 辅助
我们给出了有限N双局域全息术的希尔伯特空间的算子代数和表示理论描述。这项工作是arXiv:2602.20788 [hep-th]中有限N希尔伯特空间构造的续篇。核心结果是建立了一个不变对偶对算子代数……
英文摘要
We give an operator-algebraic and representation-theoretic description of the Hilbert spaces of finite-$N$ bilocal holography. This work is a sequel to the finite-$N$ Hilbert space construction of arXiv:2602.20788 [hep-th]. The central result is the establishment of an invariant dual-pair operator algebra: before imposing the singlet constraint the Fock space carries commuting actions of the color group and of a bilocal Lie algebra, while the projection to the singlet sector selects a single irreducible representation of the invariant Lie algebra, which we call a master algebra. The finite-$N$ trace relations, beginning with the quadratic identities studied here, are shown to become representation-theoretic identities of the selected irreducible representation. We summarize the orthogonal, symplectic and unitary cases, identify the corresponding finite-$N$ constraints, compute the singlet Casimirs, and explain how finite traces and partition functions are obtained through characters of the resulting irreducible representations. This provides a novel, previously unknown mathematical description of the singlet space.
