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arXiv · 2511.21807

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

Till Bargheer·Albert Bekov
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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.

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Till Bargheer, Albert Bekov. 2026-09-22. The Non-Planar Four-Point Integrand and Konishi Dimension in N=4 Super Yang-Mills Theory at Five Loops. https://doi.org/10.1103/l9hj-dmf1

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