Quantum BMS transformations in conformally flat space-times and holography

Abstract

We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\mathrm{AdS}}_2\times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call `superdilations'. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/CFT correspondence, we propose a bulk holographic description in semi-classical gravity that reproduces the results obtained from CFT computations. We discuss the implications of our results regarding quantum hairs of asymptotically flat (near-)extremal black holes.

arXiv comment55 pages, v2 updated to match published version

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• Charge Algebra in Al(A)dS${}_n$ Spacetimes
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Weyl Charges in Asymptotically Locally AdS${}_3$ Spacetimes
• Symmetry group at future null infinity I: Scalar theory
• The (super)conformal BMS${}_3$ algebra
• On Local and Integrated Stress-Tensor Commutators
• Quantum corrections to tidal Love number for Schwarzschild black holes
• Asymptotic symmetries in spatially flat FRW
• Supertranslations at Timelike Infinity
• On the Stress Tensor Light-ray Operator Algebra
• Enhanced Conformal $BM{S}_3$ Symmetries