SO(5) Landau models and nested Nambu matrix geometry

• Published in: Nuclear physics. B 2020-07, Vol.956, p.115012, Article 115012
• Main Author: Hasebe, Kazuki
• Format: Article
• Language: English
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/j.nuclphysb.2020.115012

The SO(5) Landau model is the mathematical platform of the 4D quantum Hall effect and provide a rare opportunity for a physical realization of the fuzzy four-sphere. We present an integrated analysis of the SO(5) Landau models and the associated matrix geometries through the Landau level projection. With the SO(5) monopole harmonics, we explicitly derive matrix geometry of a four-sphere in any Landau level: In the lowest Landau level the matrix coordinates are given by the generalized SO(5) gamma matrices of the fuzzy four-sphere satisfying the quantum Nambu algebra, while in higher Landau level the matrix geometry becomes a nested fuzzy structure realizing a pure quantum geometry with no counterpart in classical geometry. The internal fuzzy geometry structure is discussed in the view of an SO(4) Pauli-Schrödinger model and the SO(4) Landau model, where we unveil a hidden singular gauge transformation between their background non-Abelian field configurations. Relativistic versions of the SO(5) Landau model are also investigated and relationship to the Berezin-Toeplitz quantization is clarified. We finally discuss the matrix geometry of the Landau models in even higher dimensions.