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

Understand

The four-point function of length-two half-BPS operators in $\mathcal{N}=4$ SYM receives non-planar corrections starting at four loops.

• Previous work relied on the analysis of symmetries and logarithmic divergences to fix the integrand up to four constants.
• In this work, we compute those undetermined coefficients and fix the integrand completely by using the reformulation of $\mathcal{N}=4$ SYM in twistor space.
• The final integrand can be written as a combination of finite conformal integrals and we have used the method of asymptotic expansions to extract non-planar anomalous dimensions and structure constants for twist-two operators up to spin eight.