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

Abstract

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.

14 pages, 3 figures