Monodromy of multiloop integrals in $d$ dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911029293744128 |
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| author | Lee, Roman N. Pomeransky, Andrei A. |
| author_facet | Lee, Roman N. Pomeransky, Andrei A. |
| contents | We consider the monodromy group of the differential systems for multiloop integrals. We describe a simple heuristic method to obtain the monodromy matrices as functions of space-time dimension $d$. We observe that in a special basis the elements of these matrices are Laurent polynomials in $z=\exp(iπd)$ with integer coefficients, i.e., the monodromy group is a subgroup of $GL(n,\mathbb{Z}[z,1/z])$. We derive bilinear relations for monodromies in $d$ and $-d$ dimensions which follow from the twisted Riemann bilinear relations and check that the found monodromy matrices satisfy them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monodromy of multiloop integrals in $d$ dimensions Lee, Roman N. Pomeransky, Andrei A. High Energy Physics - Theory High Energy Physics - Phenomenology We consider the monodromy group of the differential systems for multiloop integrals. We describe a simple heuristic method to obtain the monodromy matrices as functions of space-time dimension $d$. We observe that in a special basis the elements of these matrices are Laurent polynomials in $z=\exp(iπd)$ with integer coefficients, i.e., the monodromy group is a subgroup of $GL(n,\mathbb{Z}[z,1/z])$. We derive bilinear relations for monodromies in $d$ and $-d$ dimensions which follow from the twisted Riemann bilinear relations and check that the found monodromy matrices satisfy them. |
| title | Monodromy of multiloop integrals in $d$ dimensions |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.18452 |