Chiral \(\Lambda \)-\(\mathfrak {bms}_4\) 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 \(\Lambda \)-\(\mathfrak {bms}_4\) algebra as their asymptotic symmetry algebra. This algebra is one of the four chiral \(\mathcal W\)-algebra extensions of \(\mathfrak {so}(2,3)\) and is a generalisation of the chiral \(\mathfrak {bms}_4\) algebra responsible for soft theorems of graviton MHV amplitudes in \({\mathbb R}^{1,3}\) gravity to the case of non-zero negative cosmological constant. The corresponding charges are shown to be finite and integrable, and realise this non-linear \({{\mathcal {W}}}\)-algebra.