De Haro, Sebastian (2017) The Invisibility of Diffeomorphisms. [Preprint]

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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 {\it 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 {\it QFT-visible} vs. {\it 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 {\it larger} than expected, and the class of QFT-invisible ones is {\it 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.

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Item Type:	Preprint
Creators:	Creators Email ORCID De Haro, Sebastian sd696@cam.ac.uk 0000-0002-3000-5967
Additional Information:	Forthcoming in Foundations of Physics
Keywords:	Asymptotic symmetries, ambient construction, gauge-gravity duality, diffeomorphism invariance, conformal geometry, philosophy of string theory
Subjects:	Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Dr Sebastian De Haro
Date Deposited:	06 Sep 2017 18:57
Last Modified:	06 Sep 2017 18:57
Item ID:	13400
Subjects:	Specific Sciences > Physics > Quantum Gravity Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Relativity Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	6 September 2017
URI:	https://philsci-archive.pitt.edu/id/eprint/13400

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• The Invisibility of Diffeomorphisms. (deposited 06 Sep 2017 18:57) [Currently Displayed]
  • The Invisibility of Diffeomorphisms. (deposited 03 Jan 2018 18:07)

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