The large $N$ limit from the lattice

Abstract

A numerical study of the string tension and of the masses of the lowest-lying glueballs is performed in SU($N$) gauge theories for $2 \le N \le 8$ in D=3+1 and $2 \le N \le 6$ in D=2+1. It is shown that for the string tension a smooth $N \to \infty$ limit exists that depends only on the 't Hooft coupling $\lambda = g^2 N$. An extrapolation of the masses of the lightest glueballs to $N = \infty$ using a power series in $1/N^2$ shows that the leading correction to the infinite $N$ value accounts for finite $N$ effects for $N$ at least as small as 3 and all the way down to N=2 in many cases. $k$-string tension ratios and possible issues connected with correlation functions at large $N$ are also discussed.