发表机构
Perimeter Institute for Theoretical Physics（Perimeter理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过解析 SO(3) 对称性的精确对角化算法大幅推进模糊球 CFT 研究，识别出三维 Ising CFT 中约 100 个原场算子（含重标量原场），并利用准空穴空间投影研究分数量子霍尔态临界点，为探索拓扑有序相纠缠的 CFT 提供通用策略。
AI 中文摘要
模糊球正则化近来已成为研究三维共形场论（CFT）的强大框架。在本工作中，我们利用对称性和希尔伯特空间结构来大幅推进该框架。我们开发了一种精确对角化算法，可解析完整的 SO(3) 旋转对称性，将计算成本降低数百倍。对于三维 Ising CFT，我们识别出约 100 个原场算子，其中包括大量此前未知的重标量原场，其标度维度最高可达 Δ≈16.5。我们还解决了先前模糊球与 bootstrap 结果之间关于奇宇称标量原场的矛盾。此外，我们识别出一支与 φ^4 拉格朗日描述中 φ^n 算子相关的标量原场分支，从恒等算子、σ、ε、ε′ 和 σ′ 开始。它们的波函数展现出半经典结构，与球面上面积保持微分同胚不变的状态密切相关。最后，我们证明涉及分数量子霍尔态的临界点可以在由相应模型量子霍尔波函数（如 Laughlin 态）的准空穴态张成的显著缩减的希尔伯特空间中研究。这提出了一种探索与拓扑有序相纠缠的 CFT 的通用策略。
英文摘要
Fuzzy-sphere regularization has recently emerged as a powerful framework for studying three-dimensional conformal field theories (CFTs). In this work, we exploit symmetry and Hilbert-space structures to substantially advance this framework. We develop an exact-diagonalization algorithm that resolves the full $\mathrm{SO}(3)$ rotational symmetry, reducing computational costs by factors of several hundred. For the three-dimensional Ising CFT, we identify around 100 primary operators, including a large number of previously unknown heavy scalar primaries up to scaling dimension $Δ\approx16.5$. We also resolve the tension between previous fuzzy-sphere and bootstrap results regarding the parity-odd scalar primary. Furthermore, we identify a branch of scalar primaries associated with $ϕ^n$ operators in the $ϕ^4$ Lagrangian description, beginning with the identity, $σ$, $ε$, $ε'$, and $σ'$. Their wave functions exhibit a semi-classical structure closely related to states invariant under area-preserving diffeomorphisms of the sphere. Finally, we show that critical points involving fractional quantum Hall states can be studied within a substantially reduced Hilbert space spanned by quasi-hole states of the corresponding model quantum Hall wave functions like the Laughlin state. This suggests a general strategy for exploring CFTs intertwined with topologically ordered phases.
Comments53 pages, 10 figures, 7 tables
