Linear confinement and AdS/QCD

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 $m_{n,S}^2\sim (n+S)$.

Figure 1

The squared masses of the first few $\rho$ resonances versus their consecutive number $n$ [34]. The straight line is the fit $m_n^2\sim n$.