A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics
Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in 2+1 dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For...
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| Format: | Article |
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Elsevier BV
2018
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| Online Access: | http://hdl.handle.net/1721.1/119657 https://orcid.org/0000-0001-7004-9609 |
| _version_ | 1811070727974027264 |
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| author | Seiberg, Nathan Witten, Edward Senthil, Todadri Wang, Chong |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Seiberg, Nathan Witten, Edward Senthil, Todadri Wang, Chong |
| author_sort | Seiberg, Nathan |
| collection | MIT |
| description | Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in 2+1 dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For example, the long distance behavior of the 2+1-dimensional analog of QED with a single Dirac fermion (a theory known as [formula omitted]) is identified with the O(2)Wilson–Fisher fixed point. The gauged version of that fixed point with a Chern–Simons coupling at level one is identified as a free Dirac fermion. The latter theory also has a dual version as a fermion interacting with some gauge fields. Assuming some of these dualities, other dualities can be derived. Our analysis resolves a number of confusing issues in the literature including how time reversal is realized in these theories. It also has many applications in condensed matter physics like the theory of topological insulators (and their gapped boundary states) and the problem of electrons in the lowest Landau level at half filling. (Our techniques also clarify some points in the fractional Hall effect and its description using flux attachment.) In addition to presenting several consistency checks, we also present plausible (but not rigorous) derivations of the dualities and relate them to 3+1-dimensional S-duality. |
| first_indexed | 2024-09-23T08:40:37Z |
| format | Article |
| id | mit-1721.1/119657 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T08:40:37Z |
| publishDate | 2018 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1196572022-09-30T10:26:21Z A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics Seiberg, Nathan Witten, Edward Senthil, Todadri Wang, Chong Massachusetts Institute of Technology. Department of Physics Senthil, Todadri Wang, Chong Building on earlier work in the high energy and condensed matter communities, we present a web of dualities in 2+1 dimensions that generalize the known particle/vortex duality. Some of the dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. For example, the long distance behavior of the 2+1-dimensional analog of QED with a single Dirac fermion (a theory known as [formula omitted]) is identified with the O(2)Wilson–Fisher fixed point. The gauged version of that fixed point with a Chern–Simons coupling at level one is identified as a free Dirac fermion. The latter theory also has a dual version as a fermion interacting with some gauge fields. Assuming some of these dualities, other dualities can be derived. Our analysis resolves a number of confusing issues in the literature including how time reversal is realized in these theories. It also has many applications in condensed matter physics like the theory of topological insulators (and their gapped boundary states) and the problem of electrons in the lowest Landau level at half filling. (Our techniques also clarify some points in the fractional Hall effect and its description using flux attachment.) In addition to presenting several consistency checks, we also present plausible (but not rigorous) derivations of the dualities and relate them to 3+1-dimensional S-duality. 2018-12-17T15:19:42Z 2018-12-17T15:19:42Z 2016-11 2018-12-04T13:49:24Z Article http://purl.org/eprint/type/JournalArticle 00034916 http://hdl.handle.net/1721.1/119657 Seiberg, Nathan, T. Senthil, Chong Wang, and Edward Witten. “A Duality Web In2+1dimensions and Condensed Matter Physics.” Annals of Physics 374 (November 2016): 395–433. https://orcid.org/0000-0001-7004-9609 http://dx.doi.org/10.1016/J.AOP.2016.08.007 Annals of Physics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Seiberg, Nathan Witten, Edward Senthil, Todadri Wang, Chong A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics |
| title | A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics |
| title_full | A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics |
| title_fullStr | A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics |
| title_full_unstemmed | A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics |
| title_short | A Duality Web in 2 + 1 Dimensions and Condensed Matter Physics |
| title_sort | duality web in 2 1 dimensions and condensed matter physics |
| url | http://hdl.handle.net/1721.1/119657 https://orcid.org/0000-0001-7004-9609 |
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