Quenched mesonic spectrum at large N

We compute the masses of the $\pi$ and of the $\rho$ mesons in the quenched approximation on a lattice with fixed lattice spacing $a \simeq 0.145
$\mathrm{f}\mathrm{m}$$forSU($N$)gaugetheorywith$N = 2,3,4,6$. We find that a simple linear expression in $1\mathrm{/}{N}^2$ correctly captures the features of the lowest-lying meson states at those values of $N$. This enables us to extrapolate to $N=\mathrm{\infty }$ the behaviour of $m_{\pi }$ as a function of the quark mass and of $m_{\rho }$ as a function of $m_{\pi }$. Our results for the latter agree within 5% with recent predictions obtained in the AdS/CFT framework.