The Topology of the AdS/CFT/Randall-Sundrum Complementarity

TL;DR

This paper explores the global geometric relationship between AdS/CFT and Randall-Sundrum theories, revealing how their differences can be understood through a comprehensive global framework that clarifies the structure of brane-worlds within AdS/CFT.

Contribution

It provides a global geometric formulation that unifies the local similarities and global differences of AdS/CFT and Randall-Sundrum models, clarifying the origin of brane-worlds.

Findings

Global structure of manifolds with infinities explained

Brane-worlds emerge naturally in the global AdS/CFT framework

Coordinate choices can obscure the true global geometry

Abstract

The background geometries of the AdS/CFT and the Randall-Sundrum theories are locally similar, and there is strong evidence for some kind of "complementarity" between them; yet the global structures of the respective manifolds are very different. We show that this apparent problem can be understood in the context of a more complete global formulation of AdS/CFT. In this picture, the brane-world arises within the AdS/CFT geometry as the inevitable consequence of recent results on the global structure of manifolds with "infinities". We argue that the usual coordinates give a misleading picture of this global structure, much as Schwarzschild coordinates conceal the global form of Kruskal-Szekeres space.