CFT$_3$ realizations of the full $L_\Lambda w_{1+\infty}$ symmetry

Determine whether nontrivial interacting CFT$_3$ theories exist that admit the full $L_\Lambda w_{1+\infty}$ algebra as exact or approximate symmetries.

Background

The paper realizes the $L_\Lambda w_{1+\infty}$ algebra semiclassically through light-ray operators and discusses its action on CFT$_3$ stress-tensor descendants. It does not establish whether any complete interacting CFT$_3$ possesses the full algebra as a symmetry.

The authors specifically raise the possibility of exact or approximate realizations and note that any such theories would need a corresponding ambitwistor-space interpretation. They also discuss, without resolving, whether integrability would be required.