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arXiv · 2506.18452

Monodromy of multiloop integrals in $d$ dimensions

Roman N. Lee·Andrei A. Pomeransky
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Abstract

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 $z=\exp(i\pi d)$ 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.

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Roman N. Lee, Andrei A. Pomeransky. 2025-06-23. Monodromy of multiloop integrals in $d$ dimensions. https://arxiv.org/abs/2506.18452

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