Kaluza-Klein reductions and AdS/Ricci-flat correspondence

TL;DR

This paper performs explicit Kaluza-Klein reductions of AdS and Minkowski spacetimes, revealing how the AdS/Ricci-flat correspondence maps individual modes in the large dimension limit, advancing holography for flat spacetimes.

Contribution

It provides the first detailed KK reductions of AdS on a torus and Minkowski on a sphere, illustrating their similarity and mode mapping in the large dimension limit.

Findings

KK reductions constructed with all massive modes

Gauge invariant variables and effective actions derived

Mode mapping becomes exact in large dimension limit

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 when the dimension of the compact space is finite.