The Non-Planar Four-Point Integrand and Konishi Dimension in N=4 Super Yang-Mills Theory at Five Loops

Abstract

We compute the complete non-planar integrand for the correlation function of four lightest scalar operators in N=4 super Yang-Mills theory at five-loop order. This is equivalent to the super-correlator of nine stress-tensor multiplets in the self-dual theory. Starting with an ansatz of f-graphs, we impose constraints from light-cone limits, and fix the remaining freedom by using the reformulation of the theory in twistor space. We develop an efficient GPU-based algorithm for the numerical evaluation of the twistor rules. As an application, we extract the five-loop non-planar anomalous dimension of the Konishi operator. Our code and result are provided in ancillary files.