Non-Renormalizability Properties of Quarter-BPS Correlators in $\mathcal{N}$=4 SYM

We study extremal and next-to-extremal four-point correlators involving general quarter-BPS operators in $\mathcal{N}$=4 Super Yang-Mills. Using a combination of $R$-symmetry considerations, operator product expansion content, and analytic superspace techniques, we show that such correlators get contributions only from operators belonging to short and semi-short multiplets. This result together with the non-renormalizability of the relevant three-point functions guarantees that all such four-point correlators are protected from quantum corrections.