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Do all nonabelian gauge theories produce short range force?
No, pure (unbroken) SU(2) Yang Mills for example is massless, i.e. long range
One can use the running of the coupling constant as a proxy for confinement. The $\beta$-function for $SU(N)$ to first order gives (see http://en.wikipedia.org/wiki/Asymptotic_freedom#Calculating_asymptotic_freedom): $$\beta_1(\alpha) = { \alpha^2 \over \pi} \left( -{11N \over 6} + {n_f \over 3} \right).$$ So for $N=3$ confinement (i.e. short range force) occurs with fewer than 16 species of fermions, but for $N=2$ it has to be fewer than 11.
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