The Holographic Bound in Anti-de Sitter Space

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.