Loop-corrected subleading soft theorem and the celestial stress tensor

We demonstrate that the one-loop exact subleading soft graviton theorem automatically follows from conservation of BMS charges, provided hard and fluxes separately represent extended algebra at null infinity. This confirms superrotations are genuine symmetries gravitational $\mathcal{S}$-matrix beyond semiclassical regime. In contrast with a previous proposal, celestial stress-tensor accounting for corrections phase space analysis does not require addition divergent counterterms. addition, we show symplectic form on radiative factorises into sectors, resulting canonical generators precisely coincide correct fluxes.