On the AdS/QCD estimates of the scalar glueball mass

TL;DR

This paper reviews holographic methods for estimating scalar glueball masses, highlighting assumptions in the AdS/QCD approach and clarifying the eigenvalue constraints in the soft-wall model.

Contribution

It clarifies the connection between spectral mass constraints and eigenvalue problems in the soft-wall AdS/QCD model for scalar glueballs.

Findings

Eigenvalue constraints correspond to spectral mass conditions.

Explicit link between Kallen-Lehmann spectral representation and bulk field equations.

Analysis of assumptions in holographic scalar glueball spectra derivations.

Abstract

We review standard holographic derivations of the scalar glueball spectra and emphasize computational assumptions which rely strongly on the original AdS/CFT correspondence, and those which are more arbitrary. In the soft-wall model, we show explicitly that the dual of the spectral mass constraint in the Kallen-Lehmann representation of the 2-point scalar gluonic correlator is an eigenvalue constraint on the motion equation of the bulk field corresponding this correlator.