Kaluza-Klein reductions and AdS/Ricci-flat correspondence
Kaluza-Klein reductions and AdS/Ricci-flat correspondence
The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat space-times on a sphere. The aim of this work is to perturbatively extend this map to general AdS and asymptotically flat solutions. A prime application for such map would be the development of holography for Minkowski spacetime. In this paper we perform a Kaluza-Klein (KK) reduction of AdS on a torus and of Minkowski on a sphere, keeping all massive KK modes. Such computation is interesting on its own, as there are relatively few examples of such explicit KK reductions in the literature. We perform both KK reductions in parallel to illustrate their similarity. In particular, we show how to construct gauge invariant variables, find the field equations they satisfy, and construct a corresponding effective action. We further diagonalize all equations and find their general solution in closed form. Surprisingly, in the limit of large dimension of the compact manifolds (torus and sphere), the AdS/RF correspondence maps individual KK modes from one side to the other. In a sequel of this paper we will discuss how the AdS/RF maps acts on general linear perturbations.
Skenderis, Konstantinos
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Caldarelli, Marco M
873ef6f9-92c0-48f6-8362-6b1bee12d540
Skenderis, Konstantinos
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Caldarelli, Marco M
873ef6f9-92c0-48f6-8362-6b1bee12d540
Skenderis, Konstantinos and Caldarelli, Marco M
(2018)
Kaluza-Klein reductions and AdS/Ricci-flat correspondence.
European Physical Journal C, 78 (590).
(doi:10.1140/epjc/s10052-018-6058-8).
Abstract
The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat space-times on a sphere. The aim of this work is to perturbatively extend this map to general AdS and asymptotically flat solutions. A prime application for such map would be the development of holography for Minkowski spacetime. In this paper we perform a Kaluza-Klein (KK) reduction of AdS on a torus and of Minkowski on a sphere, keeping all massive KK modes. Such computation is interesting on its own, as there are relatively few examples of such explicit KK reductions in the literature. We perform both KK reductions in parallel to illustrate their similarity. In particular, we show how to construct gauge invariant variables, find the field equations they satisfy, and construct a corresponding effective action. We further diagonalize all equations and find their general solution in closed form. Surprisingly, in the limit of large dimension of the compact manifolds (torus and sphere), the AdS/RF correspondence maps individual KK modes from one side to the other. In a sequel of this paper we will discuss how the AdS/RF maps acts on general linear perturbations.
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kk-v3
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Accepted/In Press date: 10 July 2018
e-pub ahead of print date: 21 July 2018
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Local EPrints ID: 422364
URI: http://eprints.soton.ac.uk/id/eprint/422364
ISSN: 1434-6044
PURE UUID: 1126e196-506d-4f4b-a80f-0370007da792
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Date deposited: 23 Jul 2018 16:30
Last modified: 16 Mar 2024 06:53
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Author:
Marco M Caldarelli
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