Correspondence principle for a brane in Minkowski space and vector mesons

TL;DR

This paper establishes a correspondence principle in Minkowski space for a 3-brane, linking bulk Poincare algebra to brane conformal algebra, and derives vector meson spectra consistent with AdS/QCD models.

Contribution

It introduces a Minkowski space correspondence principle for branes, connecting bulk symmetries to brane conformal symmetry, and computes vector meson spectra matching AdS results.

Findings

Poincare algebra reduces to conformal algebra on the brane as cosmological constant approaches zero.

Derived vector meson spectra for finite-thickness branes match truncated AdS space results.

Identified bulk mass scale M consistent with QCD and Planck scale for D=10.

Abstract

We consider a 3-brane of positive cosmological constant (de Sitter) in D-dimensional Minkowski space. We show that the Poincare algebra in the bulk yields a SO(4,2) algebra when restricted to the brane. In the limit of zero cosmological constant (flat brane), this algebra turns into the conformal algebra on the brane. We derive a correspondence principle for Minkowski space analogous to the AdS/CFT correspondence. We discuss explicitly the cases of scalar and gravitational fields. For a 3-brane of finite thickness in the transverse directions, we obtain a spectrum for vector gravitational perturbations which correspond to vector mesons. The spectrum agrees with the one obtained in truncated AdS space by de Teramond and Brodsky provided D=10 and the bulk mass scale M is of order the geometric mean of the Planck mass ($\bar M$) on the brane and $\Lambda_{QCD}$ ($M \sim (\bar M \Lambda_{QCD})^{1/2} \sim 10^9$ GeV).