Monodromy of multiloop integrals in d dimensions

A bstract 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.