Chiral $\Lambda$-$\mathfrak{bms}_4$ symmetry of 3d conformal gravity

TL;DR

This paper introduces new boundary conditions for 3d conformal gravity that realize a chiral $ ext{BMS}_4$ algebra, extending soft theorem symmetries to non-zero negative cosmological constant, with finite, integrable charges.

Contribution

It proposes mixed boundary conditions for 3d conformal gravity that admit a chiral $ ext{BMS}_4$ algebra as asymptotic symmetry, extending soft theorem symmetries to AdS-like settings.

Findings

Charges are finite and integrable.

The asymptotic symmetry algebra is a non-linear $ ext{W}$-algebra.

The boundary conditions are consistent with the variational principle.

Abstract

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 calculated using the modified covariant phase space formalism are shown to be finite and integrable, and realise this non-linear ${\cal W}$-algebra.