Structure constants in N=4 supersymmetric Yang-Mills theory and separation of variables

We propose a new framework for computing three-point functions in planar N=4 super Yang-Mills theory where these correlators take the form of multiple integrals of separation of variables type. We test this formalism at weak coupling at leading and next-to-leading orders in a noncompact SL(2) sector of the theory and all the way to next-to-next-to-leading orders for a compact SU(2) sector. We find evidence that wrapping effects can also be incorporated.