About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD.
1, Why do we need to solve QCD exactly?
Of course, solving any field theory exactly is a dream. But what I mean is why do we feel more urgent to solve exactly QCD than other theories such as $\phi^4$ theory? Is the reason that perturbation can not be used in QCD in some cases such as the confinement problem?
2, Why do we need the large N expansion?
People say that QCD is a zero-parameter theory because the coupling constant $g$ is changing with the RG flow. And to do a first approximation, we should introduce a parameter to expand in. The parameter turns out to be the $N$ in $SU(N)$. But similar arguments can be given for $\phi^4$ theory where the coupling $\lambda$ is also a RG flow dependent quantity. Then why do we naturally and comfortably expand in $\lambda$ there? And even after we introduce the large N expansion, we still do the analysis with the help of feynman diagrams which means that we already use the perturbation theory. So does it mean that the argument 'large N limit is introduced because QCD is a zero-parameter theory' incorrect and actually it is introduced simply for simplifying the calculations?
I really appreciate if someone can discuss these issus here.
The second question has been answered here. And I think the answer to the first question is exactly what I guessed in this post, partly also because QCD is very important.