FQHE and tt * geometry
Abstract Cumrun Vafa [1] has proposed a microscopic description of the Fractional Quantum Hall Effect (FQHE) in terms of a many-body Hamiltonian H invariant under four supersymmetries. The non-Abelian statistics of the defects (quasi-holes and quasi-particles) is then determined by the monodromy rep...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2019)172 |
| _version_ | 1818953061205278720 |
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| author | Riccardo Bergamin Sergio Cecotti |
| author_facet | Riccardo Bergamin Sergio Cecotti |
| author_sort | Riccardo Bergamin |
| collection | DOAJ |
| description | Abstract Cumrun Vafa [1] has proposed a microscopic description of the Fractional Quantum Hall Effect (FQHE) in terms of a many-body Hamiltonian H invariant under four supersymmetries. The non-Abelian statistics of the defects (quasi-holes and quasi-particles) is then determined by the monodromy representation of the associated tt * geometry. In this paper we study the monodromy representation of the Vafa 4-susy model. Modulo some plausible assumption, we find that the monodromy representation factors through a Temperley-Lieb/Hecke algebra with q = ± exp (πi/ν) as predicted in [1]. The emerging picture agrees with the other predictions of [1] as well. The bulk of the paper is dedicated to the development of new concepts, ideas, and techniques in tt * geometry which are of independent interest. We present several examples of these geometric structures in various contexts. |
| first_indexed | 2024-12-20T10:00:17Z |
| format | Article |
| id | doaj.art-9c1256db9d5b4badbdd772a36333c056 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T10:00:17Z |
| publishDate | 2019-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9c1256db9d5b4badbdd772a36333c0562022-12-21T19:44:21ZengSpringerOpenJournal of High Energy Physics1029-84792019-12-0120191219110.1007/JHEP12(2019)172FQHE and tt * geometryRiccardo Bergamin0Sergio Cecotti1SISSASISSAAbstract Cumrun Vafa [1] has proposed a microscopic description of the Fractional Quantum Hall Effect (FQHE) in terms of a many-body Hamiltonian H invariant under four supersymmetries. The non-Abelian statistics of the defects (quasi-holes and quasi-particles) is then determined by the monodromy representation of the associated tt * geometry. In this paper we study the monodromy representation of the Vafa 4-susy model. Modulo some plausible assumption, we find that the monodromy representation factors through a Temperley-Lieb/Hecke algebra with q = ± exp (πi/ν) as predicted in [1]. The emerging picture agrees with the other predictions of [1] as well. The bulk of the paper is dedicated to the development of new concepts, ideas, and techniques in tt * geometry which are of independent interest. We present several examples of these geometric structures in various contexts.https://doi.org/10.1007/JHEP12(2019)172AnyonsExtended SupersymmetryTopological States of Matter |
| spellingShingle | Riccardo Bergamin Sergio Cecotti FQHE and tt * geometry Journal of High Energy Physics Anyons Extended Supersymmetry Topological States of Matter |
| title | FQHE and tt * geometry |
| title_full | FQHE and tt * geometry |
| title_fullStr | FQHE and tt * geometry |
| title_full_unstemmed | FQHE and tt * geometry |
| title_short | FQHE and tt * geometry |
| title_sort | fqhe and tt geometry |
| topic | Anyons Extended Supersymmetry Topological States of Matter |
| url | https://doi.org/10.1007/JHEP12(2019)172 |
| work_keys_str_mv | AT riccardobergamin fqheandttgeometry AT sergiocecotti fqheandttgeometry |