Sub-subleading soft gravitons: New symmetries of quantum gravity?

Due to the seminal work of Weinberg, Cachazo and Strominger we know that tree level quantum gravity amplitudes satisfy three factorization constraints. Building on previous works which relate two of these constraints to symmetries of gravity at null infinity, we present strong evidence that the third constraint is also equivalent to a new set of symmetries. Our analysis suggests that the symmetry group of quantum gravity may be richer than the BMS group -or infinite dimensional extension thereof- previously considered.