Advancing Fuzzy-Sphere CFTs: SO(3)-Rotation-Resolving Exact Diagonalization, 3D Ising Heavy Primaries, and Quasi-Hole-Space Projection
Abstract
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 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≈16.5. 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 ϕn operators in the ϕ4 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.
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BibTeX
@misc{zhou2026advancing,
title = {{Advancing Fuzzy-Sphere CFTs: $\mathrmSO(3)$-Rotation-Resolving Exact Diagonalization, 3D Ising Heavy Primaries, and Quasi-Hole-Space Projection}},
author = {Zheng Zhou and Yin-Chen He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35960},
eprint = {2609.35960},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35960},
}
RIS
TY - UNPB
TI - Advancing Fuzzy-Sphere CFTs: SO(3)-Rotation-Resolving Exact Diagonalization, 3D Ising Heavy Primaries, and Quasi-Hole-Space Projection
AU - Zheng Zhou
AU - Yin-Chen He
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35960
UR - https://arxiv.org/abs/2609.35960
AB - 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 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≈16.5. 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.
ER -