Null limit of large-charge correlators in planar $\mathcal{N}=4$ Super-Yang-Mills theory

We present a conjecture for the double-logarithmic behavior of the logarithm of large-charge correlators in the null limit in planar $\mathcal{N}=4$ Super-Yang-Mills theory. Generalizing earlier results for four- and five-point functions, our proposal predicts this behavior for $n$-point functions to all loops in terms of the tilted cusp anomalous dimension. In the dual amplitude description, it reproduces the expected small-mass behavior of massive amplitudes in the equal-mass limit.