Double soft gravitons and the extended BMS charge algebra

We discuss how scattering amplitudes with multiple soft gravitons realize the BMS charge algebra on the null boundary, including a symmetry-breaking extension term once the Virasoro algebras of local superrotations are included.  We discuss the robustness of these relations under quantum corrections, and we discuss the implications of this structure for the existence of a 2D dual CFT description for 4D scattering amplitudes.