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The Invisibility of Diffeomorphisms

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:
CreatorsEmailORCID
De Haro, Sebastiansd696@cam.ac.uk0000-0002-3000-5967
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: http://philsci-archive.pitt.edu/id/eprint/13400

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