Anti-de Sitter boundary in Poincare coordinates
C. A. Ballon Bayona, Nelson R. F. Braga
TL;DR
This paper investigates the structure of the boundary in Poincare coordinates of Anti-de Sitter space, revealing differences from the global boundary and implications for the bulk-boundary correspondence.
Contribution
It clarifies the geometric relationship between Poincare and global AdS boundaries, highlighting that Poincare boundary points can lie within the bulk of AdS.
Findings
Poincare AdS boundary is not equivalent to global AdS boundary.
Poincare boundary includes points from the bulk of AdS.
Euclidean AdS admits a semi-global chart dividing the space.
Abstract
We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS) space. We map the Poincare AdS boundary to the global coordinate chart and show why this boundary is not equivalent to the global AdS boundary. The Poincare AdS boundary is shown to contain points of the bulk of the entire AdS space. The Euclidean AdS space is also discussed. In this case one can define a semi-global chart that divides the AdS space in the same way as the corresponding Euclidean Poincare chart.
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