The Yang-Baxter Sigma Model from Twistor Space
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911605317435392 |
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| author | Ashwinkumar, Meer Pal, Jitendra |
| author_facet | Ashwinkumar, Meer Pal, Jitendra |
| contents | We derive a novel two-field four-dimensional integrable field theory (IFT) from 6d holomorphic Chern-Simons theory on twistor space. The four-dimensional IFT depends on a skew-symmetric linear operator acting on a Lie algebra, and when this operator is specialised to a solution of the modified classical Yang-Baxter equation, the IFT develops a semi-local symmetry associated with this solution. The resulting 4d analogue of the Yang-Baxter sigma model is related by symmetry reduction to the well-known 2d Yang-Baxter sigma model. An important implication that we find is the embedding of the equations of motion of the 2d Yang-Baxter sigma model in the anti-self-dual Yang-Mills equations. The 6d Chern-Simons theory on twistor space can alternatively be symmetry reduced to a 4d Chern-Simons theory configuration with disorder surface defects. The latter realises the Yang-Baxter sigma model, implying a "diamond" for the Yang-Baxter sigma model obtained from twistor space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11288 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Yang-Baxter Sigma Model from Twistor Space Ashwinkumar, Meer Pal, Jitendra High Energy Physics - Theory Mathematical Physics We derive a novel two-field four-dimensional integrable field theory (IFT) from 6d holomorphic Chern-Simons theory on twistor space. The four-dimensional IFT depends on a skew-symmetric linear operator acting on a Lie algebra, and when this operator is specialised to a solution of the modified classical Yang-Baxter equation, the IFT develops a semi-local symmetry associated with this solution. The resulting 4d analogue of the Yang-Baxter sigma model is related by symmetry reduction to the well-known 2d Yang-Baxter sigma model. An important implication that we find is the embedding of the equations of motion of the 2d Yang-Baxter sigma model in the anti-self-dual Yang-Mills equations. The 6d Chern-Simons theory on twistor space can alternatively be symmetry reduced to a 4d Chern-Simons theory configuration with disorder surface defects. The latter realises the Yang-Baxter sigma model, implying a "diamond" for the Yang-Baxter sigma model obtained from twistor space. |
| title | The Yang-Baxter Sigma Model from Twistor Space |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.11288 |