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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.17551 |
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| _version_ | 1866916460208586752 |
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| author | Cole, Lewis T. Cullinan, Ryan A. Hoare, Ben Liniado, Joaquin Thompson, Daniel C. |
| author_facet | Cole, Lewis T. Cullinan, Ryan A. Hoare, Ben Liniado, Joaquin Thompson, Daniel C. |
| contents | Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $Ω$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $λ$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17551 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Integrable Deformations from Twistor Space Cole, Lewis T. Cullinan, Ryan A. Hoare, Ben Liniado, Joaquin Thompson, Daniel C. High Energy Physics - Theory 81T13, 81R25 Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $Ω$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $λ$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory. |
| title | Integrable Deformations from Twistor Space |
| topic | High Energy Physics - Theory 81T13, 81R25 |
| url | https://arxiv.org/abs/2311.17551 |