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We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these diagrams, the differential equations can thus be computed using unitarity-compatible integration-by-parts reductions, which simplify the reduction problem by avoiding integrals with higher-power propagators.
We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite se
We evaluate a Laurent expansion in dimensional regularization parameter $epsilon=(4-d)/2$ of all the master integrals for four-loop massless propagators up to transcendentality weight twelve, using a recently developed method of one of the present co
We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To sol
We investigate generating functions for the integrals over world-sheet tori appearing in closed-string one-loop amplitudes of bosonic, heterotic and type-II theories. These closed-string integrals are shown to obey homogeneous and linear differential
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the subject. Aft