Gauge theory and boundary integrability
Abstract We study the mixed topological/holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold (Σ×ℂ)/ℤ2, obtaining a description of lattice integrable systems in the presence of a boundary. By performing an order ℏ calculation we derive a formula for the the asymptotic behav...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP05(2019)195 |
| _version_ | 1818315974291488768 |
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| author | Roland Bittleston David Skinner |
| author_facet | Roland Bittleston David Skinner |
| author_sort | Roland Bittleston |
| collection | DOAJ |
| description | Abstract We study the mixed topological/holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold (Σ×ℂ)/ℤ2, obtaining a description of lattice integrable systems in the presence of a boundary. By performing an order ℏ calculation we derive a formula for the the asymptotic behaviour of K-matrices associated to rational, quasi-classical R-matrices. The ℤ2-action on Σ × ℂ fixes a line L, and line operators on L are shown to be labelled by representations of the twisted Yangian. The OPE of such a line operator with a Wilson line in the bulk is shown to give the coproduct of the twisted Yangian. We give the gauge theory realisation of the Sklyanin determinant and related conditions in the RTT presentation of the boundary Yang-Baxter equation. |
| first_indexed | 2024-12-13T09:14:03Z |
| format | Article |
| id | doaj.art-e6bf56d066ce4f1da1e8a93c9b7d260b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T09:14:03Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e6bf56d066ce4f1da1e8a93c9b7d260b2022-12-21T23:52:53ZengSpringerOpenJournal of High Energy Physics1029-84792019-05-012019515310.1007/JHEP05(2019)195Gauge theory and boundary integrabilityRoland Bittleston0David Skinner1Department of Applied Mathematics & Theoretical Physics, University of CambridgeDepartment of Applied Mathematics & Theoretical Physics, University of CambridgeAbstract We study the mixed topological/holomorphic Chern-Simons theory of Costello, Witten and Yamazaki on an orbifold (Σ×ℂ)/ℤ2, obtaining a description of lattice integrable systems in the presence of a boundary. By performing an order ℏ calculation we derive a formula for the the asymptotic behaviour of K-matrices associated to rational, quasi-classical R-matrices. The ℤ2-action on Σ × ℂ fixes a line L, and line operators on L are shown to be labelled by representations of the twisted Yangian. The OPE of such a line operator with a Wilson line in the bulk is shown to give the coproduct of the twisted Yangian. We give the gauge theory realisation of the Sklyanin determinant and related conditions in the RTT presentation of the boundary Yang-Baxter equation.http://link.springer.com/article/10.1007/JHEP05(2019)195Chern-Simons TheoriesLattice Integrable ModelsWilson, ’t Hooft and Polyakov loops |
| spellingShingle | Roland Bittleston David Skinner Gauge theory and boundary integrability Journal of High Energy Physics Chern-Simons Theories Lattice Integrable Models Wilson, ’t Hooft and Polyakov loops |
| title | Gauge theory and boundary integrability |
| title_full | Gauge theory and boundary integrability |
| title_fullStr | Gauge theory and boundary integrability |
| title_full_unstemmed | Gauge theory and boundary integrability |
| title_short | Gauge theory and boundary integrability |
| title_sort | gauge theory and boundary integrability |
| topic | Chern-Simons Theories Lattice Integrable Models Wilson, ’t Hooft and Polyakov loops |
| url | http://link.springer.com/article/10.1007/JHEP05(2019)195 |
| work_keys_str_mv | AT rolandbittleston gaugetheoryandboundaryintegrability AT davidskinner gaugetheoryandboundaryintegrability |