A chiral Λ-bms4 symmetry of AdS4 gravity

Abstract

Generalising the chiral boundary conditions of R1,3 gravity for AdS4 gravity, we derive chiral locally AdS4 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 so(2,3). This symmetry algebra coincides with the chiral bms4 algebra in the flat space limit with the corresponding solutions mapping to the space of gravitational vacua in R1,3 gravity. We posit this symmetry algebra as the chiral version of recently discovered Λ-bms4 algebra. We propose line integral charges from the bulk AdS4 gravity associated with this asymptotic symmetry algebra and show that they obey the semi-classical limit of a W-algebra. We derive this W-algebra for finite central charge c and level κ using associativity constraints of 2d CFT and find it to be isomorphic to one of quasi-superconformal algebra that existed in the literature.