Generalising the chiral boundary conditions of $\mathbb{ R}^{ 1,3}$ gravity for AdS$_4$ gravity, we derive chiral locally AdS$_4$ solutions in the Newman-Unti gauge consistent with a variational principle whose asymptotic symmetry algebra we show, to be an infinite-dimensional chiral extension of $\mathfrak{ so}(2,3)$. This symmetry algebra coincides with the chiral $\mathfrak{ bms}_4$ algebra in the flat space limit. We posit this symmetry algebra as the chiral version of recently discovered $\Lambda$-$\mathfrak{ bms}_4$ algebra. We postulate line integral charges from the bulk AdS$_4$ gravity corresponding to this chiral symmetry algebra and show that the charges obey the semi-classical limit of a $\mathcal{ W}$-algebra that includes a level $\kappa$ Kac-Moody $\mathfrak{ sl}(2,\mathbb{ R})$ current algebra. Furthermore, using the standard tools of $2d$ CFT, we derive the quantum version of this $\mathcal{ W}$-algebra which may be denoted by $\mathcal{ W}(2;(3/2)^2,1^3)$.
Categories: hep-th math-ph math.MP