Chiral Λ-bms₄ symmetry of 3d conformal gravity

We propose mixed boundary conditions for 3d conformal gravity consistent with variational principle in its second-order formalism that admit the chiral Λ-bms₄ algebra as their asymptotic symmetry algebra. This algebra is one of the four chiral W-algebra extensions of so(2,3) and is a generalisation of the chiral bms₄ algebra responsible for soft theorems of graviton MHV amplitudes in R1,3 gravity to the case of non-zero negative cosmological constant. The corresponding charges calculated using the modified covariant phase space formalism are shown to be finite and integrable, and realise this non-linear W-algebra.