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

TL;DR

This paper computes the complete non-planar four-point integrand at five loops in N=4 super Yang-Mills theory, enabling the extraction of the Konishi operator's five-loop anomalous dimension using advanced computational techniques.

Contribution

It introduces a method to determine the five-loop non-planar integrand in N=4 SYM and applies it to find the Konishi operator's anomalous dimension.

Findings

Complete five-loop non-planar integrand computed

Numerical evaluation implemented with GPU acceleration

Konishi operator's five-loop anomalous dimension obtained

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.