Bootstrapping AdS$_2 \times$ S$^2$ hypermultiplets: hidden four-dimensional conformal symmetry

We bootstrap the $4$-point amplitude of $\mathcal{N}=2$ hypermultiplets in $\text{AdS}_2 \times \text{S}^2$ at tree-level and for arbitrary external weights. We hereby explicitly demonstrate the existence of a hidden four-dimensional conformal symmetry that was used as an assumption in previous studies to derive this result.