Integrable Systems for Generalized Toric Polygons and Higgsed 5d N=1 Theories
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908901813780480 |
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| author | Kho, Minsung Lee, Kimyeong Lee, Norton Seong, Rak-Kyeong |
| author_facet | Kho, Minsung Lee, Kimyeong Lee, Norton Seong, Rak-Kyeong |
| contents | The interplay between toric Calabi-Yau 3-folds, dimer integrable systems, and 5-dimensional quantum field theories has proved fruitful. We extend this framework to generalized toric polygons (GTPs) and show that their integrable systems arise from refined birational transformations of known dimer integrable systems acting on the Casimirs and Hamiltonians as well as the Poisson structure and spectral curves. We argue that these transformations are realized as Hanany-Witten transitions producing (p,q) 5-brane webs dual to GTPs. We show that the resulting 5d N=1 theory is obtained by Higgsing a higher-rank theory whose associated toric Calabi-Yau has a toric diagram of the same shape as the GTP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19353 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrable Systems for Generalized Toric Polygons and Higgsed 5d N=1 Theories Kho, Minsung Lee, Kimyeong Lee, Norton Seong, Rak-Kyeong High Energy Physics - Theory Mathematical Physics Algebraic Geometry The interplay between toric Calabi-Yau 3-folds, dimer integrable systems, and 5-dimensional quantum field theories has proved fruitful. We extend this framework to generalized toric polygons (GTPs) and show that their integrable systems arise from refined birational transformations of known dimer integrable systems acting on the Casimirs and Hamiltonians as well as the Poisson structure and spectral curves. We argue that these transformations are realized as Hanany-Witten transitions producing (p,q) 5-brane webs dual to GTPs. We show that the resulting 5d N=1 theory is obtained by Higgsing a higher-rank theory whose associated toric Calabi-Yau has a toric diagram of the same shape as the GTP. |
| title | Integrable Systems for Generalized Toric Polygons and Higgsed 5d N=1 Theories |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2603.19353 |