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<p>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 <i>d</i>. We observe that in a special basis the elements of these matrices are Laurent polynomials in <i>z</i> = exp(<i>iπd</i>) with integer coefficients, i.e., the monodromy group is a subgroup of <i>GL</i>(<i>n</i>, <i>ℤ</i>[<i>z</i>, 1/<i>z</i>]). We derive bilinear relations for monodromies in <i>d</i> and –<i>d</i> dimensions which follow from the twisted Riemann bilinear relations and check that the found monodromy matrices satisfy them.</p>

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Monodromy of multiloop integrals in d dimensions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月1日

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  • Roman N. Lee,
  • Andrei A. Pomeransky

摘要

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, 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.