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Note on explicit construction of conformal generators on the fuzzy sphere

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arxiv 2409.08257 v1 pith:JFCDHPH4 submitted 2024-09-12 hep-th cond-mat.stat-mechcond-mat.str-el

Ruihua Fan This is my paper
classification hep-thcond-mat.stat-mechcond-mat.str-el
keywords conformalspherefuzzygeneratorsconstructiondimensionexplicitfield
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abstract

The lowest Landau level on the sphere was recently proposed as a continuum regularization of the three-dimensional conformal field theories, the so-called fuzzy sphere regularization. In this note, we propose an explicit construction of the conformal generators on the fuzzy sphere in terms of the microscopic Hamiltonian. Specifically, we construct the generators for the translation and special conformal transformation, which are used in defining the conformal primary states and thus are of special interest. We apply our method to a concrete example, the fuzzy sphere regularized three-dimensional Ising conformal field theory. We show that it can help capture all primaries with spin $\ell < 4$ and scaling dimension $\Delta < 7$. In particular, our method can clearly separate the primary from other states that differ in scaling dimension by $1\%$, making it hard otherwise based solely on using the conformal tower associated with the primaries.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Chern-Simons-matter conformal field theory on fuzzy sphere: Confinement transition of Kalmeyer-Laughlin chiral spin liquid

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  3. Conformal scalar field theory from Ising tricriticality on the fuzzy sphere

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    cond-mat.str-el 2026-02 conditional novelty 6.0 of 10

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

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