Landau Analysis in the Grassmannian
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915892645855232 |
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| author | Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd |
| author_facet | Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd |
| contents | Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discriminants and resultants are identified with Hurwitz and Chow forms of incidence varieties in products of Grassmannians. We study their degrees and factorizations, and the kinematic regimes in which the fibers of the Landau map are rational or real. Identifying this map with the amplituhedron map on positroid varieties, and the associated recursions with promotion maps, yields a geometric mechanism for the emergence of positivity and cluster structures in planar N=4 super Yang-Mills theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25454 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Landau Analysis in the Grassmannian Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd Algebraic Geometry High Energy Physics - Theory Mathematical Physics Commutative Algebra Combinatorics 14M15, 13F60, 05E14, 13P25, 14N15, 81T99 Momentum twistors for scattering amplitudes in particle physics are lines in three-space. We develop Landau analysis for Feynman integrals in this setting. The resulting discriminants and resultants are identified with Hurwitz and Chow forms of incidence varieties in products of Grassmannians. We study their degrees and factorizations, and the kinematic regimes in which the fibers of the Landau map are rational or real. Identifying this map with the amplituhedron map on positroid varieties, and the associated recursions with promotion maps, yields a geometric mechanism for the emergence of positivity and cluster structures in planar N=4 super Yang-Mills theory. |
| title | Landau Analysis in the Grassmannian |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics Commutative Algebra Combinatorics 14M15, 13F60, 05E14, 13P25, 14N15, 81T99 |
| url | https://arxiv.org/abs/2603.25454 |