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

TL;DR

This paper demonstrates that all three-dimensional conformal field theories (CFT$_3$), including those dual to quantum gravity in AdS$_4$, exhibit an $ ext{L}_ ext{Lambda}w_{1+ ext{infinity}}$ symmetry generated by the ANEC operator and its descendants, extending previous tree-level findings to the quantum regime.

Contribution

It establishes that the $ ext{L}_ ext{Lambda}w_{1+ ext{infinity}}$ symmetry acts on all CFT$_3$s, including strongly-coupled theories, via the ANEC operator and its conformal descendants.

Findings

All CFT$_3$s admit an $ ext{L}_ ext{Lambda}w_{1+ ext{infinity}}$ action.

The symmetry is generated by the ANEC operator and its conformal descendants.

This extends soft symmetry results from tree-level to quantum regimes.

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.