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I've bumped into the study of the $SU(N)$ theory in the large-$N$ limit. I'm wondering in which way the study of this Yang-Mills theory, can give contribution to QCD with gauge group $SU(3)$, i.e. $N=3$ Any suggestion?

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Maybe I've figure out something about that. QCD is an asymptotically free theory, so while for the high energy regime, consider the perturbative method, expanding around $g=0$, is perfectly consistent, for the low energy scales this approach becomes useless. An attempt to manage this problem, is to consider an expansion in terms of the parameter $\frac{1}{N}$. Doing so the leading term is equal for every $SU(N)$ theory, and so for QCD, and this term is the only contribution in the large-$N$ case.

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