Quenched mesonic spectrum at large N

TL;DR

This study calculates the masses of pion and rho mesons in SU(N) gauge theories for N=2,3,4,6 using lattice simulations, and finds a linear relation in 1/N^2 that allows extrapolation to infinite N, aligning with AdS/CFT predictions.

Contribution

It introduces a simple linear model in 1/N^2 to describe meson masses across different N and extrapolates to N=∞, connecting lattice results with holographic predictions.

Findings

Linear 1/N^2 relation captures meson mass features

Extrapolated N=∞ results agree with AdS/CFT predictions within 5%

Provides insights into large N meson spectrum behavior

Abstract

We compute the masses of the $\pi$ and of the $\rho$ mesons in the quenched approximation on a lattice with fixed lattice spacing $a \simeq 0.145 \ \mathrm{fm}$ for SU($N$) gauge theory with $N = 2,3,4,6$. We find that a simple linear expression in $1/N^2$ correctly captures the features of the lowest-lying meson states at those values of $N$. This enables us to extrapolate to $N = \infty$ 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.