Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory
The Abelian Chern-Simons theory is considered on a cylindrical spacetime R×D, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a curved background a Kaç-Moody algebra exists, with the same central charge as in...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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American Physical Society
2021
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| _version_ | 1797100180558839808 |
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| author | Bertolini, E Gambuti, G Maggiore, N |
| author_facet | Bertolini, E Gambuti, G Maggiore, N |
| author_sort | Bertolini, E |
| collection | OXFORD |
| description | The Abelian Chern-Simons theory is considered on a cylindrical spacetime R×D, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a curved background a Kaç-Moody algebra exists, with the same central charge as in the flat case, which henceforth depends neither on the bulk metric nor on the geometry of the boundary. The holographically induced theory on the 2D boundary is topologically protected, in the sense that it describes a Luttinger liquid, no matter which the bulk metric is. The main result of this paper is that a remnant of the 3D bulk theory resides in the chiral velocity of the edge modes, which is not a constant like in the flat bulk case, but it is local, depending on the determinant of the induced metric on the boundary. This result may provide a theoretical framework for the recently observed accelerated chiral bosons on the edge of some Hall systems. |
| first_indexed | 2024-03-07T05:34:05Z |
| format | Journal article |
| id | oxford-uuid:e3426178-85b0-4164-a116-0e949dafba0b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:34:05Z |
| publishDate | 2021 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:e3426178-85b0-4164-a116-0e949dafba0b2022-03-27T10:07:55ZNotes from the bulk: Metric dependence of the edge states of Chern-Simons theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e3426178-85b0-4164-a116-0e949dafba0bEnglishSymplectic ElementsAmerican Physical Society2021Bertolini, EGambuti, GMaggiore, NThe Abelian Chern-Simons theory is considered on a cylindrical spacetime R×D, in a not necessarily flat Lorentzian background. As in the flat bulk case with planar boundary, we find that also on the radial boundary of a curved background a Kaç-Moody algebra exists, with the same central charge as in the flat case, which henceforth depends neither on the bulk metric nor on the geometry of the boundary. The holographically induced theory on the 2D boundary is topologically protected, in the sense that it describes a Luttinger liquid, no matter which the bulk metric is. The main result of this paper is that a remnant of the 3D bulk theory resides in the chiral velocity of the edge modes, which is not a constant like in the flat bulk case, but it is local, depending on the determinant of the induced metric on the boundary. This result may provide a theoretical framework for the recently observed accelerated chiral bosons on the edge of some Hall systems. |
| spellingShingle | Bertolini, E Gambuti, G Maggiore, N Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory |
| title | Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory |
| title_full | Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory |
| title_fullStr | Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory |
| title_full_unstemmed | Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory |
| title_short | Notes from the bulk: Metric dependence of the edge states of Chern-Simons theory |
| title_sort | notes from the bulk metric dependence of the edge states of chern simons theory |
| work_keys_str_mv | AT bertolinie notesfromthebulkmetricdependenceoftheedgestatesofchernsimonstheory AT gambutig notesfromthebulkmetricdependenceoftheedgestatesofchernsimonstheory AT maggioren notesfromthebulkmetricdependenceoftheedgestatesofchernsimonstheory |