The Holographic Bound in Anti-de Sitter Space

TL;DR

This paper explores the holographic bound in Anti-de Sitter space, linking bulk infrared effects to boundary ultraviolet effects, and clarifies the bound's physical interpretation within the AdS/CFT correspondence.

Contribution

It provides a physical interpretation of the holographic bound in AdS/CFT, connecting infrared bulk effects to ultraviolet boundary effects.

Findings

The holographic bound corresponds to the boundary theory's information limit per Planck area.

Infrared effects in the bulk are reflected as ultraviolet effects in the boundary theory.

The paper clarifies the physical basis of the holographic principle in AdS space.

Abstract

The correspondence between string theory in Anti-de Sitter space and super Yang Mills theory is an example of the Holographic principle according to which a quantum theory with gravity must be describable by a boundary theory. However, arguments given so far are incomplete because, while the bulk theory has been related to a boundary theory, the holographic bound saying that the boundary theory has only one bit of information per Planck area has not been justified. We show here that this bound is the physical interpretation of one of the unusual aspects of the correspondence between Anti-de Sitter space and the boundary conformal field theory, which is that infrared effects in the bulk theory are reflected as ultraviolet effects in the boundary theory.