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We define and study asymptotic Killing and conformal Killing vectors in$d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\rmAdS}_2\times S^{d-2}$. We construct the associated quantum charges for anarbitrary CFT and show they satisfy a closed algebra that includes the BMS as asub-algebra (i.e. supertranslations and superrotations) plus a noveltransformation we call `superdilations'. We study representations of thisalgebra in the Hilbert space of the CFT, as well as the action of the finitetransformations obtained by exponentiating the charges. In the context of theAdS/CFT correspondence, we propose a bulk holographic description insemi-classical gravity that reproduces the results obtained from CFTcomputations. We discuss the implications of our results regarding quantumhairs of asymptotically flat (near-)extremal black holes.

Quantum BMS transformations in conformally flat space-times and holography