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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.12486 |
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| _version_ | 1866915496023031808 |
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| author | Jarov, Seraphim |
| author_facet | Jarov, Seraphim |
| contents | This paper studies novel four-dimensional integrable field theories that are deformations of self-dual Yang-Mills. They are engineered by considering holomorphic Chern-Simons and BF type theories on covers of twistor space obtained by pulling back the vector bundle $\mathcal{O}(1)^2\to\mathbb{CP}^1$ to hyperelliptic or elliptic curves. Compactifying to 4d yields an integrable theory, which in the examples I study, are determined to leading order. The form of the higher-order corrections are bootstrapped, and I argue that the index structure and coefficients of these terms are fixed by integrability. The celestial chiral algebras of these theories are shown to live on hyper-elliptic and elliptic curves, respectively. Symmetry reducing these integrable deformations to 2d yields an example of a hyperelliptic and elliptic integrable model governing a deformation of Hitchin's equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher genus twistor spaces and the celestial torus Jarov, Seraphim High Energy Physics - Theory This paper studies novel four-dimensional integrable field theories that are deformations of self-dual Yang-Mills. They are engineered by considering holomorphic Chern-Simons and BF type theories on covers of twistor space obtained by pulling back the vector bundle $\mathcal{O}(1)^2\to\mathbb{CP}^1$ to hyperelliptic or elliptic curves. Compactifying to 4d yields an integrable theory, which in the examples I study, are determined to leading order. The form of the higher-order corrections are bootstrapped, and I argue that the index structure and coefficients of these terms are fixed by integrability. The celestial chiral algebras of these theories are shown to live on hyper-elliptic and elliptic curves, respectively. Symmetry reducing these integrable deformations to 2d yields an example of a hyperelliptic and elliptic integrable model governing a deformation of Hitchin's equations. |
| title | Higher genus twistor spaces and the celestial torus |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.12486 |