EVERY CFT$_3$ HAS AN $ \mathcal{L}_{\Lambda}w_{1+\infty}$ SYMMETRY

Recently a one-parameter family of deformed $\mathcal{L} w_{1+\infty}$ soft symmetry algebras, denoted $\mathcal{L}_{\Lambda}w_{1+\infty}$, acting on tree-level gravitational theories in AdS$_4$ has been discovered. Here we show that all CFT$_3$s, including those dual to quantum gravity on AdS$_4$, admit an $\mathcal{L}_{\Lambda}w_{1+\infty}$ action generated by the ANEC operator, its conformal descendants and their commutators. This extends the previous tree-level results on these soft symmetries to the strongly-coupled quantum regime.