Linear confinement and AdS/QCD

Abstract

In a theory with linear confinement, such as QCD, the masses squared ${m}_{n,S}^{2}$ 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 an 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 ${m}_{n,S}^{2}\ensuremath{\sim}(n+S)$.