Positivity and Cluster Structures in Landau Analysis
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911546360201216 |
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| author | Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd |
| author_facet | Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd |
| contents | Landau analysis in momentum twistor space can be formulated as the study of varieties of lines in three-dimensional projective space, together with their projections and discriminants. Within this framework, we define enumerative invariants (LS degrees) that count leading singularities. Leading Landau singularities (LS discriminants) arise as discriminants detecting the collision of leading singularities. We uncover a recursive mechanism underlying Landau singularities, governed by substitution maps between Grassmannians. Applying this framework, we prove positivity and factorization into cluster variables for the LS discriminant of a large class of Landau diagrams at arbitrary loop order. This provides a first-principles explanation for the emergence of positivity and cluster algebra structures in the singularities of planar N=4 super Yang-Mills theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25493 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positivity and Cluster Structures in Landau Analysis Hollering, Benjamin Mazzucchelli, Elia Parisi, Matteo Sturmfels, Bernd High Energy Physics - Theory Landau analysis in momentum twistor space can be formulated as the study of varieties of lines in three-dimensional projective space, together with their projections and discriminants. Within this framework, we define enumerative invariants (LS degrees) that count leading singularities. Leading Landau singularities (LS discriminants) arise as discriminants detecting the collision of leading singularities. We uncover a recursive mechanism underlying Landau singularities, governed by substitution maps between Grassmannians. Applying this framework, we prove positivity and factorization into cluster variables for the LS discriminant of a large class of Landau diagrams at arbitrary loop order. This provides a first-principles explanation for the emergence of positivity and cluster algebra structures in the singularities of planar N=4 super Yang-Mills theory. |
| title | Positivity and Cluster Structures in Landau Analysis |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.25493 |