Generalized GMP Algebra for Three-Dimensional Quantum Hall Fluids of Extended Objects
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918343262339072 |
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| author | Palumbo, Giandomenico |
| author_facet | Palumbo, Giandomenico |
| contents | We develop a geometric framework for three-dimensional quantum Hall fluids of extended objects (quasi-strings) in the presence of a strong three-form background field associated with a bundle gerbe. In the strong-field regime, fast internal dynamics is frozen and the low-energy kinematics is governed by generalized guiding-center variables consisting of vectorial and tensorial coordinates. We show that these guiding-center variables obey a noncommutative geometry giving rise to a three-dimensional generalization of the Girvin-MacDonald-Platzman (GMP) algebra for projected density operators. Moreover, we relate this algebra to the canonical quantization of a topological BF+BB theory whose level is identified with the Dixmier-Douady invariant. Our results clarify the structure of incompressible quantum Hall-type phases and their geometric and topological features in three spatial dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized GMP Algebra for Three-Dimensional Quantum Hall Fluids of Extended Objects Palumbo, Giandomenico High Energy Physics - Theory Mesoscale and Nanoscale Physics Strongly Correlated Electrons We develop a geometric framework for three-dimensional quantum Hall fluids of extended objects (quasi-strings) in the presence of a strong three-form background field associated with a bundle gerbe. In the strong-field regime, fast internal dynamics is frozen and the low-energy kinematics is governed by generalized guiding-center variables consisting of vectorial and tensorial coordinates. We show that these guiding-center variables obey a noncommutative geometry giving rise to a three-dimensional generalization of the Girvin-MacDonald-Platzman (GMP) algebra for projected density operators. Moreover, we relate this algebra to the canonical quantization of a topological BF+BB theory whose level is identified with the Dixmier-Douady invariant. Our results clarify the structure of incompressible quantum Hall-type phases and their geometric and topological features in three spatial dimensions. |
| title | Generalized GMP Algebra for Three-Dimensional Quantum Hall Fluids of Extended Objects |
| topic | High Energy Physics - Theory Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2602.15664 |