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The four-point function of length-two half-BPS operators in $\mathcal{N}=4$SYM receives non-planar corrections starting at four loops. Previous workrelied on the analysis of symmetries and logarithmic divergences to fix theintegrand up to four constants. In this work, we compute those undeterminedcoefficients and fix the integrand completely by using the reformulation of$\mathcal{N}=4$ SYM in twistor space. The final integrand can be written as acombination of finite conformal integrals and we have used the method ofasymptotic expansions to extract non-planar anomalous dimensions and structureconstants for twist-two operators up to spin eight. Some of the results werealready know in the literature and we have found agreement with them.

Non-planar data of $\mathcal N=4$ SYM