Large $N$ scaling and factorization in SU($N$) Yang-Mills gauge theory

TL;DR

This study uses advanced lattice simulations and the Yang-Mills gradient flow to non-perturbatively verify large N scaling and factorization in SU(N) gauge theories, confirming theoretical predictions with high precision.

Contribution

It provides the most precise non-perturbative verification of large N scaling and factorization in SU(N) gauge theories to date, using extensive Monte Carlo simulations for N=3,4,5,6,8.

Findings

Large N scaling is confirmed with high precision.

Factorization in the large N limit is validated.

Large Wilson loops exhibit O(1/N^2) corrections.

Abstract

The large $N$ limit of SU($N$) gauge theories is well understood in perturbation theory. Also non-perturbative lattice studies have yielded important positive evidence that 't Hooft's predictions are valid. We go far beyond the statistical and systematic precision of previous studies by making use of the Yang-Mills gradient flow and detailed Monte Carlo simulations of SU($N$) pure gauge theories in 4 dimensions. With results for $N=3,4,5,6,8$ we study the limit and the approach to it. We pay particular attention to observables which test the expected factorization in the large $N$ limit. The investigations are carried out both in the continuum limit and at finite lattice spacing. Large $N$ scaling is verified non-perturbatively and with high precision; in particular, factorization is confirmed. For quantities which only probe distances below the typical confinement length scale, the coefficients of the $1/N$ expansion are of $\mathrm{O}(1)$, but we found that large (smoothed) Wilson loops have rather large $\mathrm{O}(1/N^2)$ corrections. The exact size of such corrections does, of course, also depend on what is kept fixed when the limit is taken.