Extensivity Versus Holography in Anti-de Sitter Spaces

TL;DR

This paper explores how the dimensionality in the AdS/CFT correspondence exhibits holographic properties at the quantum level, particularly through high temperature behavior and black hole emergence.

Contribution

It demonstrates that the high temperature behavior of systems in AdS/CFT reveals holographic dimensionality and shows how black holes lead to dimensional screening at the quantum level.

Findings

High temperature behavior indicates holographic dimensionality

AdS black holes act as master fields at high temperature

Extra dimensions are screened in the black hole's excluded volume

Abstract

We study the dimensionality manifested in the AdS/CFT correspondence. We show that the dimensionality as expressed by the high temperature behavior of a system has a holographic nature also at the quantum level. The emergence of the AdS black hole as a master field at high temperature leads to the screening of the extra dimensions in its excluded volume.