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. Our result for the integrand suggests a sharpened $f$-graph genus conjecture. As an application, we extract the five-loop non-planar anomalous dimension of the Konishi operator, whose 1/N_c^2 term is entirely given in terms of odd zeta values of transcendentality five and higher. Our code and result are provided in ancillary files.

11 pages, 5 figures, 3 tables. Code and result provided in ancillary files. v2: typos fixed. v3: typos fixed, published version