Compact AdS space, Brane geometry and the AdS/CFT correspondence

TL;DR

This paper explores the relationship between compact AdS spaces and brane-generated geometries within the AdS/CFT framework, analyzing their boundary conditions and physical consistency.

Contribution

It demonstrates the equivalence of boundary roles in compact AdS and brane geometries and introduces a coordinate system linking spatial infinity to horizons.

Findings

Boundary in compact AdS is equivalent to asymptotic region in brane space

A second coordinate chart reveals spatial infinity as a horizon in brane systems

Both formulations are physically consistent in the context of the Cauchy problem

Abstract

The AdS/CFT correspondence can be realized in spaces that are globally different but share the same asymptotic behavior. Two known cases are: a compact AdS space and the space generated by a large number of coincident branes. We discuss the physical consistency, in the sense of the Cauchy problem, of these two formulations. We show that the role of the boundary in the compact AdS space is equivalent to that of the flat asymptotic region in the brane space. We also show, by introducing a second coordinate chart for the pure AdS space, that a point at its spatial infinity corresponds to a horizon in the brane system.