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Constructing the Infrared Conformal Generators on the Fuzzy Sphere

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arxiv 2409.02998 v2 pith:LSEKDZS7 submitted 2024-09-04 hep-th cond-mat.stat-mech

Giulia Fardelli , A. Liam Fitzpatrick , Emanuel Katz This is my paper
classification hep-thcond-mat.stat-mech
keywords generatorsconformalenergyaccuracycorrectionsfuzzymomentumoperators
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abstract

We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how to extract these generators using the energy momentum tensor, which is complicated by the fact that one does not have a priori access to the energy momentum tensor of the CFT limit but rather must construct it numerically. We discuss and quantitatively analyze the main sources of corrections to the conformal generators due to the breaking of scale-invariance at finite energy, and develop efficient methods for removing these corrections. The resulting generators have matrix elements that match CFT predictions with accuracy varying from sub-percent level for the lowest-lying states up to several percent accuracy for states with dimension $\sim 5$ with $N=16$ fermions. We show that the generators can be used to accurately identify primary operators vs descendant operators in energy ranges where the spectrum is too dense to do the identification solely based on the approximate integer spacing within conformal multiplets.

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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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    A bilayer quantum Hall fuzzy-sphere model, tuned to an Ising tricritical point, realizes the conformally coupled free scalar CFT, verified by matching spectra, operator content, and bosonic algebra.

  4. 3d Conformal Field Theories via Fuzzy Sphere Algebra

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

    The fuzzy-sphere density-mode algebra is a genuine Lie algebra, but a direct density-mode realization of the 3d conformal algebra so(3,2) exists only for the two-electron system.

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

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    Fuzzy-sphere Hamiltonians realize the O(2), O(3) and O(4) Wilson-Fisher and free-scalar CFTs numerically, with spectra and correlators matching conformal bootstrap expectations.

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