Linear Confinement and AdS/QCD

TL;DR

The paper argues that linear confinement implies that $m_{n,S}^2$ should grow linearly with spin $S$ and radial excitation $n$; it demonstrates that such a spectrum can be reproduced in a putative five-dimensional AdS/QCD dual and translates the asymptotically linear $m^2$ behavior into strong IR constraints on the dual theory. Assuming the existence of this dual, the authors show that the simplest model respecting these constraints yields $m_{n,S}^2 \sim (n+S)$. This work connects phenomenological linear Regge trajectories in QCD to IR boundary conditions in holographic models, guiding the construction of AdS/QCD duals that capture high-excitation meson spectra.

Abstract

In a theory with linear confinement, such as QCD, the masses squared m^2 of mesons with high spin S or high radial excitation number n are expected, from semiclassical arguments, to grow linearly with S and n. We show that this behavior can be reproduced within a putative 5-dimensional theory holographically dual to QCD (AdS/QCD). With the assumption that such a dual theory exists and describes highly excited mesons as well, we show that asymptotically linear m^2 spectrum translates into a strong constraint on the INFRARED behavior of that theory. In the simplest model which obeys such a constraint we find m^2 ~ (n+S).

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