Characterizing Cohen-Macaulay One-Loop Feynman Integrals
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917148299886592 |
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| author | Michaelsen, Kyrill Tellander, Felix |
| author_facet | Michaelsen, Kyrill Tellander, Felix |
| contents | We study the generalized hypergeometric systems, in the sense of Gel'fand, Kapranov, and Zelevinsky, associated with one-loop Feynman integrals, and determine when their rank is independent of space-time dimension and propagator powers. This is equivalent to classifying when the associated affine semigroup ring is Cohen-Macaulay. For massive one-loop integrals, we prove necessary and sufficient conditions for Cohen-Macaulayness, generalizing previous results on normality for these rings. We show that for Feynman integrals, the Cohen-Macaulay property is fully determined by an integer linear program built from the Newton polytope of the integrand and find a graphical description of its solutions. Furthermore, we provide a sufficient condition for Cohen-Macaulayness of general one-loop integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Cohen-Macaulay One-Loop Feynman Integrals Michaelsen, Kyrill Tellander, Felix High Energy Physics - Theory Mathematical Physics Algebraic Geometry We study the generalized hypergeometric systems, in the sense of Gel'fand, Kapranov, and Zelevinsky, associated with one-loop Feynman integrals, and determine when their rank is independent of space-time dimension and propagator powers. This is equivalent to classifying when the associated affine semigroup ring is Cohen-Macaulay. For massive one-loop integrals, we prove necessary and sufficient conditions for Cohen-Macaulayness, generalizing previous results on normality for these rings. We show that for Feynman integrals, the Cohen-Macaulay property is fully determined by an integer linear program built from the Newton polytope of the integrand and find a graphical description of its solutions. Furthermore, we provide a sufficient condition for Cohen-Macaulayness of general one-loop integrals. |
| title | Characterizing Cohen-Macaulay One-Loop Feynman Integrals |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2512.13820 |