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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2508.07777 |
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| _version_ | 1866918122059988992 |
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| author | Xie, Dan |
| author_facet | Xie, Dan |
| contents | We study Seiberg-Witten (SW) geometries for rank-two theories, encompassing 4D field theories as well as 5D and 6D Kaluza-Klein (KK) theories. The singular model for each SW geometry is derived from a one-parameter family of algebraic curves $y^2 = f(x,t)$, where $t$ parametrizes one dimension of Coulomb branch moduli space. The functional form of $f(x,t)$ is systematically determined through analysis of singular fibers at $t=\infty$. Two powerful computational methods enable this determination: a): Liu's algorithm for determining singular fibers from local equation; b): The canonical resolution method for fiber degeneration. Our construction provides not only a complete description of known solutions but also establishes a robust framework for generating new theories. This methodology proves particularly valuable for the systematic exploration of 5D and 6D theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On classification of rank two theories with eight supercharges Part III: Seiberg-Witten geometry Xie, Dan High Energy Physics - Theory Algebraic Geometry We study Seiberg-Witten (SW) geometries for rank-two theories, encompassing 4D field theories as well as 5D and 6D Kaluza-Klein (KK) theories. The singular model for each SW geometry is derived from a one-parameter family of algebraic curves $y^2 = f(x,t)$, where $t$ parametrizes one dimension of Coulomb branch moduli space. The functional form of $f(x,t)$ is systematically determined through analysis of singular fibers at $t=\infty$. Two powerful computational methods enable this determination: a): Liu's algorithm for determining singular fibers from local equation; b): The canonical resolution method for fiber degeneration. Our construction provides not only a complete description of known solutions but also establishes a robust framework for generating new theories. This methodology proves particularly valuable for the systematic exploration of 5D and 6D theories. |
| title | On classification of rank two theories with eight supercharges Part III: Seiberg-Witten geometry |
| topic | High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2508.07777 |