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The O(N) Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere

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arxiv 2512.02234 v2 pith:T3VTYOIM submitted 2025-12-01 cond-mat.str-el cond-mat.stat-mechhep-th

The O(N) Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere

Wenhan Guo , Zheng Zhou , Tzu-Chieh Wei , Yin-Chen He This is my paper
classification cond-mat.str-el cond-mat.stat-mechhep-th
keywords conformaltheoriescftsfieldfree-scalarmodelnumericalwilson-fisher
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The fuzzy-sphere regularization is an emerging numerical and theoretical technique for studying conformal field theories (CFTs). In this paper, we apply it to the $O(N)$ vector model, one of the most prominent theories for critical behavior in three space-time dimensions. We construct a model that realizes the $O(N)$ Wilson-Fisher and free-scalar CFTs for general $N$. For $N=2,3,4$, we present numerical evidence including the operator spectra and correlation functions in agreement with conformal symmetry and conformal bootstrap results.

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Cited by 5 Pith papers

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  1. Studying 3D O(N) Surface CFT on the Fuzzy Sphere

    cond-mat.str-el 2026-04 conditional novelty 7.0

    Boundary CFT spectra, OPE coefficients, and central charges are extracted for normal and ordinary boundaries of the 3D O(2) and O(3) Wilson-Fisher fixed points via fuzzy-sphere state-operator correspondence, with conf...

  2. Fortuitous Universality of Bose-Kondo Impurities

    cond-mat.str-el 2026-04 unverdicted novelty 7.0

    Bose-Kondo impurities with spins S=1/2, 1, and 3/2 each flow to distinct stable interacting conformal defects despite sharing the same symmetry and anomaly.

  3. Conformal Data for the $O(2)$ Wilson-Fisher CFT in $(2+1)$-Dimensional Spacetime from Exact Diagonalization and Matrix Product States on the Fuzzy Sphere

    cond-mat.str-el 2026-04 unverdicted novelty 6.0

    Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.

  4. Toward Entanglement Bootstrap for Conformal Field Theory in Any Dimension

    hep-th 2026-06 unverdicted novelty 5.0

    Proposes and numerically tests a reconstructed Hamiltonian for approximate CFT ground states in any dimension that recovers CFT spectral properties.

  5. Lectures on Semiclassical Methods for Composite Operators

    hep-th 2026-06 unverdicted novelty 3.0

    Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.