Abstract
We define and study asymptotic Killing and conformal Killing vectors in d-dimensional Minkowski, (A)dS, ℝ × Sd−1 and AdS2× Sd−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.
Highlights
Back in the sixties, Bondi, van der Burg, Metzner and Sachs (BMS) studied the symmetry algebra of asymptotically flat space-times at future and past null infinity I± [1,2,3], and to their surprise, found that instead of the finite dimensional Poincaré algebra, space-time translations were enhanced to an infinite dimensional sub-algebra they called supertranslations
The structure of BMS symmetry has appeared at the horizon of classical black holes solutions [14, 15], and it has been suggested it supplies the necessary additional structure to provide a possible resolution of the black hole information paradox [16, 17]
The purpose of this paper is to study in detail quantum aspects of BMS symmetry in conformally flat space-times, aiming towards possible applications to holography and black hole physics
Summary
Bondi, van der Burg, Metzner and Sachs (BMS) studied the symmetry algebra of asymptotically flat space-times at future and past null infinity I± [1,2,3], and to their surprise, found that instead of the finite dimensional Poincaré algebra, space-time translations were enhanced to an infinite dimensional sub-algebra they called supertranslations. We call BMS algebra to the enhanced version containing both supertranslations and superrotations.. BMS asymptotic symmetries have been investigated from several different promising perspectives. Studies of the gravitational scattering matrix in Minkowski [10] have lead to interesting relations between BMS symmetry, soft theorems [11], and the socalled gravitational memory effects [12] (see [13] for a review and further references). The structure of BMS symmetry has appeared at the horizon of classical black holes solutions [14, 15], and it has been suggested it supplies the necessary additional structure to provide a possible resolution of the black hole information paradox [16, 17]
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