AdS space compactification and holographic mapping in the AdS/CFT correspondence

TL;DR

This paper explores how compactifying AdS space affects quantum field spectra and establishes a holographic mapping between bulk and boundary states, reproducing QCD scaling and estimating glueball mass ratios.

Contribution

It introduces a holographic mapping in AdS/CFT that accounts for space compactification and applies it to QCD phenomena.

Findings

Discretization of bulk field spectrum due to compactification

One-to-one bulk-boundary state mapping established

Reproduction of high energy QCD scaling and glueball mass ratio estimates

Abstract

Physical consistency of quantum fields in anti-de Sitter space time requires that the space must be compactified by the inclusion of a boundary where appropriate conditions are imposed. An interpretation for the presence of this boundary is found taking AdS as a limiting case of the space generated by a large number of coincident branes. The compactification of AdS leads to a discretization of the spectrum of bulk fields. As a consequence, we find a one to one mapping between the quantum states of scalar fields in AdS bulk and boundary. Using this mapping as an approximation for the dual relation between string dilaton field and scalar QCD glueballs the high energy QCD scaling is reproduced. We also use this map to estimate the ratio of scalar glueball masses.