Kaluza–Klein reductions and AdS/Ricci-flat correspondence

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 spacetimes 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.

Unitarization from geometry

“…From this we can read off the following degrees of freedom: 5 An alternative to algebraically fixing the Stückelberg symmetry is to form gauge-invariant combinations orderby-order in powers of the fields, e.g., as in Refs. [28,29]. The lowest-order gauge-invariant combination in this case isà Aa µ ≡ A Aa µ − ∂µA Aa .…”

A correspondence between Ricci-flat Kerr and Kaluza-Klein AdS black hole

“…The celebrated AdS/CFT correspondence [8] is the different type, relating weakly-coupled gravity in the anti-de Sitter (AdS) background to some strongly coupled conformal field theory (CFT) on its boundary, an example of the alternatives to compactification [11] In this paper, we study a new type of correspondence proposed in [12]. (See also [13,14].) It relates pure Einstein gravity on a sphere to Einstein gravity with a negative cosmological constant Λ on a suitable torus.…”

A Correspondence between Ricci-flat Kerr and Kaluza-Klein AdS Black Hole

“…The celebrated AdS/CFT correspondence [7] is the different type, relating weakly-coupled gravity in the anti-de Sitter (AdS) background to some strongly coupled conformal field theory (CFT) on its boundary, an example of the alternatives to compactification [8] In this paper, we study a new type of correspondence proposed in [9]. (See also [10,11]. )…”