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I am having a hard time getting to grips with the statement that $$g_{0}(a) \to 0 \text{ as } a \to 0$$ where $g_{0}$ is the bare coupling in lattice QCD and $a$ the lattice spacing.

How come this does not mean that the continuum limit of lattice QCD is a perturbative (or even free) theory? How does one compute non-perturbative quantities in the continuum limit if $g_{0} \to 0$?

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The bare coupling vanishes in the continuum limit, because the renormalized quantities are associated with measurements over very large scales (compared to the lattice spacing). One way to think about this is that since QCD is confining, the coupling at the scale of the lattice spacing must vanish if the coupling at the continuum scale is to remain finite. Otherwise, the 'tension' associated with Wilson loops would be unphysically large (i.e. infinite) in the continuum limit.

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