Quantum statistics and spacetime surgery
© 2020 The Author(s) It is known that quantum statistics of quasiparticles in 2+1 spacetime dimensions beget anyons, beyond the familiar statistics of bosons and fermions, while Verlinde formula dictates the consistent anyon statistics. In 3+1 dimensions, although quasiparticles cannot be anyonic, e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/132532 |
| _version_ | 1811093456496361472 |
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| author | Wang, Juven Wen, Xiao-Gang Yau, Shing-Tung |
| author_facet | Wang, Juven Wen, Xiao-Gang Yau, Shing-Tung |
| author_sort | Wang, Juven |
| collection | MIT |
| description | © 2020 The Author(s) It is known that quantum statistics of quasiparticles in 2+1 spacetime dimensions beget anyons, beyond the familiar statistics of bosons and fermions, while Verlinde formula dictates the consistent anyon statistics. In 3+1 dimensions, although quasiparticles cannot be anyonic, extended quasi-excitations like strings can have anyonic string statistics. In this work, we first introduce the fusion and braiding data of particle and string excitations creatable from the operators of (world-) lines/sheets, and all are well-defined in gapped states of matter with intrinsic topological orders. We then apply the geometric-topology surgery theory to derive a set of quantum surgery formulas analogous to Verlinde's constraining the fusion and braiding quantum statistics of anyonic particle and anyonic string excitations in 2+1 and 3+1 dimensions, essential for the theory of bulk topological orders and potentially correlated to bootstrap boundary physics. |
| first_indexed | 2024-09-23T15:45:28Z |
| format | Article |
| id | mit-1721.1/132532 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:45:28Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1325322021-09-21T03:10:06Z Quantum statistics and spacetime surgery Wang, Juven Wen, Xiao-Gang Yau, Shing-Tung © 2020 The Author(s) It is known that quantum statistics of quasiparticles in 2+1 spacetime dimensions beget anyons, beyond the familiar statistics of bosons and fermions, while Verlinde formula dictates the consistent anyon statistics. In 3+1 dimensions, although quasiparticles cannot be anyonic, extended quasi-excitations like strings can have anyonic string statistics. In this work, we first introduce the fusion and braiding data of particle and string excitations creatable from the operators of (world-) lines/sheets, and all are well-defined in gapped states of matter with intrinsic topological orders. We then apply the geometric-topology surgery theory to derive a set of quantum surgery formulas analogous to Verlinde's constraining the fusion and braiding quantum statistics of anyonic particle and anyonic string excitations in 2+1 and 3+1 dimensions, essential for the theory of bulk topological orders and potentially correlated to bootstrap boundary physics. 2021-09-20T18:22:53Z 2021-09-20T18:22:53Z 2020-11-16T19:23:22Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/132532 en 10.1016/J.PHYSLETB.2020.135516 Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Elsevier BV Elsevier |
| spellingShingle | Wang, Juven Wen, Xiao-Gang Yau, Shing-Tung Quantum statistics and spacetime surgery |
| title | Quantum statistics and spacetime surgery |
| title_full | Quantum statistics and spacetime surgery |
| title_fullStr | Quantum statistics and spacetime surgery |
| title_full_unstemmed | Quantum statistics and spacetime surgery |
| title_short | Quantum statistics and spacetime surgery |
| title_sort | quantum statistics and spacetime surgery |
| url | https://hdl.handle.net/1721.1/132532 |
| work_keys_str_mv | AT wangjuven quantumstatisticsandspacetimesurgery AT wenxiaogang quantumstatisticsandspacetimesurgery AT yaushingtung quantumstatisticsandspacetimesurgery |