Quantum BMS transformations in conformally flat space-times and holography

TL;DR

This paper explores the extension of BMS symmetries in various conformally flat spacetimes, introduces a new 'superdilations' transformation, and connects these symmetries to holography and black hole quantum hairs.

Contribution

It defines and analyzes quantum charges associated with asymptotic symmetries, including a novel 'superdilations' transformation, and links these to holography and black hole physics.

Findings

BMS algebra extended with superdilations

Quantum charges form a closed algebra in CFT

Holographic description reproduces CFT results

Abstract

We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\rm AdS}_2\times S^{d-2}$. 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.