Monodromy of multiloop integrals in d dimensions

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(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.