The Invisibility of Diffeomorphisms

Abstract

I examine the relationship between $(d+1)$-dimensional Poincaré metrics and $d$-dimensional conformal manifolds, from both mathematical and physical perspectives. The results have a bearing on several conceptual issues relating to asymptotic symmetries, in general relativity and in gauge-gravity duality, as follows: (1: Ambient Construction) I draw from the remarkable work by Fefferman and Graham (1985, 2012) on conformal geometry, in order to prove two propositions and a theorem that characterise the classes of diffeomorphisms that qualify as gravity-invisible. I define natural notions of gravity-invisibility (strong, weak, and simpliciter) which apply to the diffeomorphisms of Poincaré metrics in any dimension. (2: Dualities) I apply the notions of invisibility to gauge-gravity dualities: which, roughly, relate Poincaré metrics in $d+1$ dimensions to QFTs in $d$ dimensions. I contrast QFT-visible vs. QFT-invisible diffeomorphisms: those gravity diffeomorphisms that can, respectively cannot, be seen from the QFT. The QFT-invisible diffeomorphisms are the ones which are relevant to the hole argument in Einstein spaces. The results on dualities are surprising, because the class of QFT-visible diffeomorphisms is larger than expected, and the class of QFT-invisible ones is smaller than expected, or usually believed, i.e. larger than the PBH diffeomorphisms in Imbimbo et al. (2000). I also give a general derivation of the asymptotic conformal Killing equation, which has not appeared in the literature before.

arXiv comment28+7 pages, 1 figure. v2: published version, minor corrections

References in corpus (21)

• Gauge Theory Correlators from Non-Critical String Theory
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The Dynamics of General Relativity
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Lecture Notes on Holographic Renormalization
• The dS/CFT Correspondence
• Soft Hair on Black Holes
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• Asymptotically Anti-de Sitter spacetimes and their stress energy tensor
• Diffeomorphisms and Holographic Anomalies
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• Asymptotics with a positive cosmological constant: I. Basic framework
• Most general AdS_3 boundary conditions
• Conceptual Aspects of Gauge/Gravity Duality
• Asymptotic Symmetries and Charges in De Sitter Space
• Non-relativistic holography from Horava gravity
• Emergence in Holographic Scenarios for Gravity
• The supersymmetric NUTs and bolts of holography
• Dualities and Emergent Gravity: Gauge/Gravity Duality
• Dual Gravitons in AdS4/CFT3 and the Holographic Cotton Tensor